PIC32MX: FFT of Analog Input - Revision history

AndrewDai: /* IFFT Example Plot */

2010-05-20T18:30:35Z

IFFT Example Plot

2010-05-20T18:30:04Z

Overview

2010-05-20T18:29:39Z

IFFT Code

2010-05-20T17:54:39Z

IFFT Example Plot

2010-05-20T17:54:23Z

IFFT Code

2010-05-20T17:53:41Z

IFFT Circuit

2010-05-20T17:50:06Z

Overview

2010-05-20T17:46:16Z

2010-05-20T17:45:32Z

2010-03-01T20:20:17Z

← Older revision		Revision as of 18:30, 20 May 2010
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	This waveform is a 30Hz sine wave superimposed on a 40Hz sine wave with the same amplitude and phase. As one can see, the FFT amplitude line up almost exactly. The phase graph has some discrepancy, but this can be easily fixed by changing the FFT phase vector to float, rather than int16. It is ok to use int16 here because the vector is not being inputted into the mips_fft algorithm. And finally, the inverse FFT matches up very nicely with the original signal, very little information is lost.		This waveform is a 30Hz sine wave superimposed on a 40Hz sine wave with the same amplitude and phase. As one can see, the FFT amplitude line up almost exactly. The phase graph has some discrepancy, but this can be easily fixed by changing the FFT phase vector to float, rather than int16. It is ok to use int16 here because the vector is not being inputted into the mips_fft algorithm. And finally, the inverse FFT matches up very nicely with the original signal, very little information is lost.

	[[Image: ~~IFFTwaveforms~~.png\|border\|700px]]		[[Image: IFFTwaveforms2.png\|border\|700px]]

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 With the PIC32, an inverse FFT can also be computed.  Inverse FFT is a function that converts a frequency domain signal into a time domain signal. Inverse FFTs actually use the same algorithm as FFTs except with some scaling and conjugation or time reversal (depending on the algorithm).  The second half of this page shows how you can create an analog signal, takes the FFT of that signal, and then take the inverse FFT of the result to try and obtain the original waveform back. The data is all sent to MATLAB via RS232 and compared to MATLAB's computational results for accuracy.
-The C code and Matlab code for this program can be downloaded [[Media: IFFTcode.zip | here]].
+The C code and Matlab code for this program can be downloaded [[Media: IFFTcode2.zip | here]].
 == FFT Circuit ==

@@ Line 534: / Line 534: @@
 == IFFT Code ==
-The code for both MATLAB and the PIC32 can be found [[Media: IFFTcode.zip | here]].  The code is very similar to the code found above.  There are two main differences:
+The code for both MATLAB and the PIC32 can be found [[Media: IFFTcode2.zip | here]].  The code is very similar to the code found above.  There are two main differences:
 . There is now an "analog output."  This is basically a PWM that is filtered through a low pass filter.  The pulse widths are modified very quickly, with the width of the pulse directly related to the amplitude of the output.  Thus, a very short pulse is the same as the trough of the sine wave and a long pulse is the same as the peak of the wave.

@@ Line 541: / Line 541: @@
 == IFFT Example Plot ==
+This waveform is a 30Hz sine wave superimposed on a 40Hz sine wave with the same amplitude and phase.  As one can see, the FFT amplitude line up almost exactly.  The phase graph has some discrepancy, but this can be easily fixed by changing the FFT phase vector to float, rather than int16.  It is ok to use int16 here because the vector is not being inputted into the mips_fft algorithm.  And finally, the inverse FFT matches up very nicely with the original signal, very little information is lost.
+[[Image: IFFTwaveforms.png|border|700px]]

@@ Line 533: / Line 533: @@
 == IFFT Code ==
+The code for both MATLAB and the PIC32 can be found [[Media: IFFTcode.zip | here]].  The code is very similar to the code found above.  There are two main differences:
+. There is now an "analog output."  This is basically a PWM that is filtered through a low pass filter.  The pulse widths are modified very quickly, with the width of the pulse directly related to the amplitude of the output.  Thus, a very short pulse is the same as the trough of the sine wave and a long pulse is the same as the peak of the wave.
+. This is more of a tip, but after the analog inputs are stored in the sample array, they are scaled up by a factor, in this case, 256.  All this does is increase the range of the values.  I found this to give results that align much better with MATLAB's results.  The reason for this is that the mips_fft16 algorithm accepts int16 and int32 data the best.  However, int data types can lose information since they round to the nearest integer.  Thus, we can scale all the inputs to make them larger, thus yielding more accuracy (it is as if we added a few more decimal places).
 == IFFT Example Plot ==

@@ Line 527: / Line 527: @@
 == IFFT Circuit ==
+This circuit is very similar to the preview FFT circuit, except that it includes a low pass filter.  This filter integrates the PWM signal that is output from pin D0 and creates a continuous, analog signal.
+[[Image:IFftSchematic.png|border|700px]]
 == IFFT Code ==

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 Commented C code and Matlab code are provided at the bottom of this page and can be downloaded [[Media: Lab5FFTcode.zip | here]].
-== Circuit ==
+== FFT Circuit ==
 Beyond simple inputs and outputs, there is no special circuitry required for computing FFTs.  The signal is inserted into pin B4 on the PIC and must be below VREF on the PIC (currently configured to 3.3 V).  For data output, the PIC uses RS-232 communication.  Three connections need to be made with the RS-232:
@@ Line 22: / Line 22: @@
 [[Image:FftSchematic.png]]
-== Code ==
+== FFT Code ==
 The following is the source code to be programmed onto the PIC.  If unfamiliar, see [[HelloWorld_PIC32 | here]] for a guide to creating a .hex file with MPLAB and [[Directions_to_Load_Files_to_PIC32_with_HID_Bootloader | here]] for directions to load files to the PIC.  It first establishes inputs, outputs and RS-232 communication.  When prompted with a 'p' (as written, it is prompted automatically by Matlab), the PIC computes the FFT then sends the magnitude portion of the single-sided FFT and the raw samples to Matlab.
@@ Line 502: / Line 502: @@
 </pre>
-==Example Plots==
+==FFT Example Plots==
 Here is an example using a 500 Hz sine wave input.
 [[Image: FFT_500_sin.jpg|border|700px]]

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-== Original Assignment ==
-'''Do not erase this section!'''
-Your assignment is to read in several cycles of a periodic signal from a function generator (e.g., a sine wave or a square wave), perform an FFT on your samples using your PIC32, and send back the results to a PC to display.  Try this for 256 samples and 1024 samples, and determine how long it takes to compute the FFT for each, once you have collected the data.  Verify that the results make sense according to the input signals you've used; for example, a sine wave should have all power at the chosen frequency, while a square wave will have much of the power at the frequency of the wave, but power at other frequencies, too.)  Check out the MPLAB C32 Libraries manual to learn more about the dsplib_dsp.h, which you must include.  Try both mips_fft16 and mips_fft32.
 == Overview ==
 A fast Fourier transform (FFT) is a method to calculate a discrete Fourier transform (DFT).  More information about [http://en.wikipedia.org/wiki/Fast_Fourier_transform FFTs]  and [http://en.wikipedia.org/wiki/Discrete_Fourier_transform DFTs] can be found on wikipedia (linked).