Difference between revisions of "Component: Fast Fourier Transform (FFT) (DSP)"

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| width="20%" style="color: gray;" | Author
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| width="20%" style="color:gray;" | Author
 
| Matrix Ltd
 
| Matrix Ltd
 
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| 1.1
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| 1.2
 
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| width="20%" style="color:gray;" | Category
 
| DSP
 
| DSP
 
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==Fast Fourier Transform (FFT) component==
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Provides a way of converting a buffer full of time domain data into frequency domain data. The output of the FFT is a set of frequency bins which correspond to the frequencies present in the signal. The number of frequency bins is equal to half the input buffer size with each bin being responsible for a portion of the frequency up to 1/2 the nyquist.
  
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==[[File:Component Icon f804a7bd_0280_4ff7_ab75_63be77fb2af3.png|Image]] Fast Fourier Transform (FFT) component==
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==Component Pack==
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Provides a way of converting a buffer full of time domain data into frequency domain data.
 
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The output of the FFT is a set of frequency bins which correspond to the frequencies present in the signal.
 
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The number of frequency bins is equal to half the input buffer size with each bin being responsible for a portion of the frequency up to 1/2 the nyquist.
 
  
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==Examples==
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DSP
  
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FFT Example File
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==Detailed description==
  
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{{Fcfile|FFT_Test.fcfx|FFT Example}}
 
  
  
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Example takes 256 analogue readings using an ADC input and then passes the collection of 256 samples to the FFT function which produces 128 individual frequency banks which are then plotted from left to right on the graphical LCD.
 
  
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[[File:FFT.jpg]]
 
  
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==Downloadable macro reference==
 
  
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===<span style="font-weight: normal;"><u><tt>ReadFrequencyBank</tt></u></span>===
 
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''<span style="color:red;">No additional information</span>''
 
  
  
  
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'''Parameters'''
 
  
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:[[Variable Types|UINT]] ''BankIdx''
 
  
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''No detailed description exists yet for this component''
  
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'''Return value'''
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==Examples==
  
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:[[Variable Types|BYTE]]
 
  
  
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===<span style="font-weight: normal;"><u><tt>FFT</tt></u></span>===
 
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''<span style="color:red;">No additional information</span>''
 
  
  
  
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'''Parameters'''
 
  
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:''This macro has no parameters''
 
  
  
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'''Return value'''
 
  
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:''This call does not return a value''
 
  
  
  
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==Simulation macro reference==
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Example takes two adjustable frequency sine wave inputs and combines them and then passes the collection of 256 samples to the FFT function which produces 128 individual frequency banks which are then plotted from left (lowest frequency) to right (highest frequency) using an XY chart component.
  
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''This component does not contain any simulation macros''
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{{Fcfile|FFT_Test.fcfx|FFT Example}}
  
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Frequency output for a set of data
  
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==Property reference==
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[[File:FFT.jpg]]
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<span style="font-weight: normal;"><u>Buffer Manager</u></span>
 
  
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This property is of type ''Fixed list of ints'' and can be referenced with the variable name ''buffer_manager''.
 
  
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''<span style="color:red;">No additional information</span>''
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Frequency banks can be worked out by using the sample frequency and buffer size. The number of frequency banks is equal to the number of samples divided by 2 minus 1. We subtract the one because bank 0 is always empty and so can be discounted.
  
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FrequencyBanks = (SampleCount / 2) - 1
  
  
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<span style="font-weight: normal;"><u>Input</u></span>
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The frequency ranges present inside a bank can be worked out as follows.
  
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This property is of type ''Fixed list of ints'' and can be referenced with the variable name ''input_a''.
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FreqMin = ((SampleRate / 2) / (SampleCount / 2)) * Bank
  
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''<span style="color:red;">No additional information</span>''
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FreqMax = ((SampleRate / 2) / (SampleCount / 2)) * (Bank + 1)
  
  
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For example if we sample at 10KHz and collect 256 samples then frequency bank 10 would represent any frequencies in the range of 390.6Hz to 429.7Hz.
  
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<span style="font-weight: normal;"><u>Output Real</u></span>
 
  
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This property is of type ''Fixed list of ints'' and can be referenced with the variable name ''output_c''.
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Here is a spreadsheet document that will calculate the frequencies present in each bank. The highlighted green fields are editable and will update the rest of the values.
  
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''<span style="color:red;">No additional information</span>''
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[[File:FFT_Frequency_Bank_Calculator.xls]]
  
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[[File:FFTBanks.jpg]]
  
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==Downloadable macro reference==
  
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<span style="font-weight: normal;"><u>Output Imaginary</u></span>
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{| class="wikitable" style="width:60%; background-color:#FFFFFF;"
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|-
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| width="10%" align="center" style="background-color:#D8C9D8;" align="center" | [[File:Fc9-comp-macro.png]]
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| width="90%" style="background-color:#D8C9D8; color:#4B008D;" | '''ReadFrequencyBank'''
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|-
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| colspan="2" | Reads the value from one of the frequency banks after the FFT conversion has been performed.  Valid frequency banks range from 1 to the allocated buffer size / 2 assuming the buffers are sized to be equal to a power of 2.&nbsp;
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|-
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|-
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| width="10%" align="center" | [[File:Fc9-u16-icon.png]] - UINT
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| width="90%" | BankIdx
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|-
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| colspan="2" | &nbsp;
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|-
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| width="10%" align="center" style="border-top: 2px solid #000;" | [[File:Fc9-u16-icon.png]] - UINT
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| width="90%" style="border-top: 2px solid #000;" | ''Return''
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|}
  
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This property is of type ''Fixed list of ints'' and can be referenced with the variable name ''output_i''.
 
  
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''<span style="color:red;">No additional information</span>''
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{| class="wikitable" style="width:60%; background-color:#FFFFFF;"
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|-
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| width="10%" align="center" style="background-color:#D8C9D8;" align="center" | [[File:Fc9-comp-macro.png]]
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| width="90%" style="background-color:#D8C9D8; color:#4B008D;" | '''FFT'''
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|-
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| colspan="2" | Performs the data conversion from time based data to frequency based data. Takes a full buffer input and converts it into real and imaginary frequency data ready for you to read the individual frequency bins.&nbsp;
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|-
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|-
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| width="10%" align="center" style="border-top: 2px solid #000;" | [[File:Fc9-void-icon.png]] - VOID
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| width="90%" style="border-top: 2px solid #000;" | ''Return''
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|}
  
  
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{| class="wikitable" style="width:60%; background-color:#FFFFFF;"
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|-
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| width="10%" align="center" style="background-color:#D8C9D8;" align="center" | [[File:Fc9-comp-macro.png]]
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| width="90%" style="background-color:#D8C9D8; color:#4B008D;" | '''QueueData'''
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|-
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| colspan="2" | Takes a single value from the buffer input and stores it, once there are enough values queued up it returns a 1.&nbsp;
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|-
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|-
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| width="10%" align="center" | [[File:Fc9-bool-icon.png]] - BOOL
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| width="90%" | ProcessWhenFull
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|-
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| colspan="2" | 0 = Do Nothing when Buffer is full, 1 = Auto call FFT macro when Buffer is full&nbsp;
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|-
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| width="10%" align="center" style="border-top: 2px solid #000;" | [[File:Fc9-bool-icon.png]] - BOOL
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| width="90%" style="border-top: 2px solid #000;" | ''Return''
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|}
  
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<span style="font-weight: normal;"><u>Accuracy</u></span>
 
  
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This property is of type ''Fixed list of ints'' and can be referenced with the variable name ''FFT_accuracy''.
 
  
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''<span style="color:red;">No additional information</span>''
 
  
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==Property reference==
  
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{| class="wikitable" style="width:60%; background-color:#FFFFFF;"
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<span style="font-weight: normal;"><u>Bit Depth</u></span>
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|-
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| width="10%" align="center" style="background-color:#D8C9D8;" | [[File:Fc9-prop-icon.png]]
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This property is of type ''Fixed list of ints'' and can be referenced with the variable name ''bit_depth''.
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| width="90%" style="background-color:#D8C9D8; color:#4B008D;" | '''Properties'''  
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|-
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''<span style="color:red;">No additional information</span>''
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|-
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| width="10%" align="center" | [[File:Fc9-type-16-icon.png]]
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| width="90%" | Connect To
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|-
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<span style="font-weight: normal;"><u>Sample Rate</u></span>
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| colspan="2" | DSP component with output buffer to collect our data from.&nbsp;
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|-
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This property is of type ''Floating point'' and can be referenced with the variable name ''sample_rate''.
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| width="10%" align="center" | [[File:Fc9-type-21-icon.png]]
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| width="90%" | Buffer Size
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''<span style="color:red;">No additional information</span>''
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|-
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| colspan="2" | Number of individual elements the buffer can store, must be a power of 2, default 256.&nbsp;
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|-
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| width="10%" align="center" | [[File:Fc9-type-16-icon.png]]
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<span style="font-weight: normal;"><u>Nyquist Frequency</u></span>
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| width="90%" | Buffer Type
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|-
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This property is of type ''Floating point'' and can be referenced with the variable name ''nyquist''.
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| colspan="2" | Sets the buffer data type.&nbsp;
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|-
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''<span style="color:red;">No additional information</span>''
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| width="10%" align="center" | [[File:Fc9-type-7-icon.png]]
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| width="90%" | Filter Input Data
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|-
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| colspan="2" | Applies a hamming window filter to the time domain sample data to provide better frequency detection.&nbsp;
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<span style="font-weight: normal;"><u>Frequency Bin Count</u></span>
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|-
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| width="10%" align="center" style="background-color:#EAE1EA;" | [[File:Fc9-conn-icon.png]]
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This property is of type ''Signed integer'' and can be referenced with the variable name ''bin_count''.
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| width="90%" style="background-color:#EAE1EA; color:#4B008D;" | Calculations
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|-
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''<span style="color:red;">No additional information</span>''
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|-
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| width="10%" align="center" | [[File:Fc9-type-15-icon.png]]
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| width="90%" | Sample Rate
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|-
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<span style="font-weight: normal;"><u>Frequency Bin Size (Hz)</u></span>
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| colspan="2" | Sample rate used to perform simple calculations like nyquist and bin size.&nbsp;
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|-
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This property is of type ''Floating point'' and can be referenced with the variable name ''bin_size''.
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| width="10%" align="center" | [[File:Fc9-type-15-icon.png]]
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| width="90%" | Nyquist Frequency
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''<span style="color:red;">No additional information</span>''
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|-
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| colspan="2" | The maximum frequency that can theoretically be detected by the FFT component assuming the sample rate is setup correctly.&nbsp;
 +
|-
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| width="10%" align="center" | [[File:Fc9-type-14-icon.png]]
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| width="90%" | Frequency Bin Count
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|-
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| colspan="2" | The number of frequency bins that the component will provide.&nbsp;
 +
|-
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| width="10%" align="center" | [[File:Fc9-type-15-icon.png]]
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| width="90%" | Frequency Bin Size (Hz)
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|-
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| colspan="2" | The frequency range covered by each frequency bin.&nbsp;
 +
|}

Latest revision as of 17:19, 9 November 2022

Author Matrix Ltd
Version 1.2
Category DSP


Fast Fourier Transform (FFT) component

Provides a way of converting a buffer full of time domain data into frequency domain data. The output of the FFT is a set of frequency bins which correspond to the frequencies present in the signal. The number of frequency bins is equal to half the input buffer size with each bin being responsible for a portion of the frequency up to 1/2 the nyquist.

Component Pack

DSP

Detailed description

No detailed description exists yet for this component

Examples

Example takes two adjustable frequency sine wave inputs and combines them and then passes the collection of 256 samples to the FFT function which produces 128 individual frequency banks which are then plotted from left (lowest frequency) to right (highest frequency) using an XY chart component.

FC6 Icon.png FFT Example

Frequency output for a set of data

FFT.jpg


Frequency banks can be worked out by using the sample frequency and buffer size. The number of frequency banks is equal to the number of samples divided by 2 minus 1. We subtract the one because bank 0 is always empty and so can be discounted.

FrequencyBanks = (SampleCount / 2) - 1


The frequency ranges present inside a bank can be worked out as follows.

FreqMin = ((SampleRate / 2) / (SampleCount / 2)) * Bank

FreqMax = ((SampleRate / 2) / (SampleCount / 2)) * (Bank + 1)


For example if we sample at 10KHz and collect 256 samples then frequency bank 10 would represent any frequencies in the range of 390.6Hz to 429.7Hz.


Here is a spreadsheet document that will calculate the frequencies present in each bank. The highlighted green fields are editable and will update the rest of the values.

File:FFT Frequency Bank Calculator.xls

FFTBanks.jpg

Downloadable macro reference

Fc9-comp-macro.png ReadFrequencyBank
Reads the value from one of the frequency banks after the FFT conversion has been performed. Valid frequency banks range from 1 to the allocated buffer size / 2 assuming the buffers are sized to be equal to a power of 2. 
Fc9-u16-icon.png - UINT BankIdx
 
Fc9-u16-icon.png - UINT Return


Fc9-comp-macro.png FFT
Performs the data conversion from time based data to frequency based data. Takes a full buffer input and converts it into real and imaginary frequency data ready for you to read the individual frequency bins. 
Fc9-void-icon.png - VOID Return


Fc9-comp-macro.png QueueData
Takes a single value from the buffer input and stores it, once there are enough values queued up it returns a 1. 
Fc9-bool-icon.png - BOOL ProcessWhenFull
0 = Do Nothing when Buffer is full, 1 = Auto call FFT macro when Buffer is full 
Fc9-bool-icon.png - BOOL Return



Property reference

Fc9-prop-icon.png Properties
Fc9-type-16-icon.png Connect To
DSP component with output buffer to collect our data from. 
Fc9-type-21-icon.png Buffer Size
Number of individual elements the buffer can store, must be a power of 2, default 256. 
Fc9-type-16-icon.png Buffer Type
Sets the buffer data type. 
Fc9-type-7-icon.png Filter Input Data
Applies a hamming window filter to the time domain sample data to provide better frequency detection. 
Fc9-conn-icon.png Calculations
Fc9-type-15-icon.png Sample Rate
Sample rate used to perform simple calculations like nyquist and bin size. 
Fc9-type-15-icon.png Nyquist Frequency
The maximum frequency that can theoretically be detected by the FFT component assuming the sample rate is setup correctly. 
Fc9-type-14-icon.png Frequency Bin Count
The number of frequency bins that the component will provide. 
Fc9-type-15-icon.png Frequency Bin Size (Hz)
The frequency range covered by each frequency bin. 
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