The TV framework described below was used as a spectrum analyser by adding a fixed point FFT routine. The routine works in 16:16 fixed format. A 512 point complex FFT takes 410,000 cpu cycles (with no optimization) or about 6.8 milliseconds. If we include the time to Hanning window the signal and compute the magnitude of the complex output, the process takes 454,800 cpu cycles (with no optimization), or about 7.6 milliseconds. Running the compiler at optimization level 1 (highest free compiler level) reduces the number of cpu cycles to 146,000, or about 2.4 milliseconds for Hanning-FFT-magnutude calculation. The two images show a sine signal and a square wave captured at 900,000 samples/sec. There is some aliasing of the square wave so the peaks are not clean, but you can see the 1/f spectrum. The magnitude of the FFT is approximated as
|amplitude|=max(|Re|,|Im|)+0.4*min(|Re|,|Im|). This approximation is accurate within about 4%.
Taking the log of the magnitude using a fast approximation (Generation of Products and Quotients Using Approximate Binary Logarithms for Digital Filtering Applications, IEEE Transactions on Computers 1970 vol.19 Issue No.02) gives more resolution at lower amplitudes( code). Evaluation of the algorithm as a matlab program is here. The following images give the matlab comparison of exact and approximate log for noise, and a sinewave FFT on the PIC32.
--NTSC video is an old standard, but is still used in North America for closed circuit TV. It is fairly simple to generate a black/white NTSC signal. Also, the frame buffer for a 1-bit, 256x200 pixel image is only 1600 words (6400 bytes) of RAM. Chapter 13 of Programming 32-bit Microcontrollers in C: Exploring the PIC32 by Lucio Di Jasio was very useful. I used Di Jasio's method of generating sync pulses using one output-compare unit. Video is sent to the SPI controller using DMA bursts from memory (also similar to Di Jasio), but DMA timing-start control was implemented using another output-compare unit rather than chaining two DMA channels. This allowed easy control of video content timing. Timer2 is ticking away with an match time equal to one video line time. Ouput-compare 2 is slaved to timer2 to generate a series of pulses at the line-rate. The duration of the OC2 pulses (for vertical sync) is controlled by the Timer2 match ISR in which a simple state machine is running, but the pulse durations are not dependent on ISR execution time. Output-compare 3 is also slaved to timer2 and set up to generate an interrupt at a time appropriate for the end of the NTSC back porch, at which time the DMA burst to the SPI port starts. I got best video stability when the core is running at 60 MHz and the peripheral bus running at 30 MHz. The first example is just a bounding ball with some text. The example requires that the ascii character header file be in the project folder. The DAC which combines the SYNC and video signal and adjusts to levels to standard video is:
--The second example is a particle system explosion. Without doing any space optimization 1500 particles (along with screen buffer) use up memory. All the positions can be updated in every frame. Giving each particle a high initial velocity, and high drag makes a nice cloud.
-- The third example is a particle system fountain, which is a slight modification of the explosion. I optimized the point-draw and one ISR for more efficient execution. Frame update now takes 7.2 mSec. Video. The overhead for NTSC TV signal generation is about 5 microSec per 63.5 microSec line, or about 8%. You should use this optimized version for an intensive animation. A small variation makes the particle system fire to the side. Video.
--The fourth example turns on the ADC to make an oscilloscope. The ADC is set up to trigger from the timer3 compare match signal, but without turning on an ISR. A DMA channel transfer is then triggered by the ADC done signal to dump the ADC results to memory at up to 900 Ksamples/sec. This ADC hardware process runs at the same time as the video update hardware process, so video is not disturbed. CPU load is small so there is time to draw the ADC waveform to the screen. It would be straightforward to add a button state machine for scope control and a FFT. The following image is captured from the NTSC screen and shows the scope running at 900 Ksamples/sec and displaying a frequency estimate. Video is running at 500 Ksamples/sec ADC rate.
-- The fifth example is a vector variation of the scope. Drawing all the vectors slows the redraw down so that the scope is updated 30 times/sec.
Video is running at 900 Ksamples/sec. Still image below.
