![fft max msp fft max msp](https://live.staticflickr.com/188/439677114_14a56bd67b_z.jpg)
It's going to have a DC component, an average offset of 1.25. In this simple example here is going to have three components.
#Fft max msp plus
In this case here, this signal is going to repeat over and over again from minus infinity to plus infinity any periodic way we can decompose it into a sum of sinusoids.
![fft max msp fft max msp](https://dobrian.github.io/cmp/topics/fourier-transform/spectral_gate_pfft.png)
And so what we're going to do is if we have enough frequencies, we can decompose any periodic. To show you the essence of what a transform is, is we take an arbitrary waveform here, an arbitrary waveform sampled in time. And so we've talked about this frequency resolution in the previous slide, which is fs divided by N, all right. I can properly represent in my digital samples signal components from DC up to but not including 1/2 fs, all right. And according to the Nyquist theorem, if I sample it fs, then I can distinguish. And so we cannot resolve in time delta t, the time resolution is 1 over the sampling rate. There's a finite number of sets The finite number of values from which this can be selected, that is the precision.Īnd the sampling rate in this picture is 1 Hertz. There is a resolution of values, the difference between two values that I can distinguish. In other words, there is a finite range of values. Now, since we did sampling, all the things we've talked about before still happened. And the essence of the Fast Fourier transform is to take N of these samples and then perform the transform on it to get the resolution. This is obviously discrete both in amplitude and in time. And that's to remind you that sampling takes a continuous waveform shown as the solid line here and replaces it with discrete samples. We've actually done this exact same slide before.
![fft max msp fft max msp](https://docs.cycling74.com/static/max8/images/f64e0e01bac62562b2478b732cc40027.png)
And the essence of this Discrete Fourier Transform as implemented in the Fast Fourier technique, it is the essence of how a spectrum analyzer works, which is why we're studying it here in this section, all right. So as the number of samples goes up, so does the execution speed. So you don't have to buy an expensive spectrum analyzer, you can use the 432 itself to calculate this amplitude versus frequency plot and using this algorithm called the Fast Fourier Transform, all right. And as we saw in a previous video, we see that the choice of the sampling rate and the size will affect the frequency resolution, the difference between two frequencies that we can distinguish which is going to be the sampling rate divided by this size, OK?īecause we've got microcontrollers, we're actually going to look at an implementation that actually executes on the MSP 432. And rather than take an infinite number of samples, we will take a finite number of samples. So inherent in this process is we are sampling. We can look at filtering, et cetera, to try to lower the noise or increase the signal. And in that way, we can look at things like signal to noise ratio. And we can use the spectrum analyzer to look at the shape and frequencies of our signal of what we're trying to measure and then compare that to the shape and frequencies of our noise. And a spectrum analyzer is something that calculates the amplitude versus frequency of the data. Now, this is the basic way in which a spectrum analyzer works. And this allows us to observe the signal in the frequency domain. And then perform an algorithm, a Discrete Fourier Transform or a Fast Fourier Transform on any of those samples to create a sequence of frequency amplitudes, the frequency values, capital A sub k. These are our samples as a function of time. And the basic idea of transform is to take a time dependent signal here, a voltage, a position, a temperature, or something, sample it at a regular rate like we've be doing all chapter to get a sequence of time dependent numbers. The Fast Fourier Transform is a fast algorithm to calculate the Discrete Fourier Transform. And in this lecture, I'd like to talk about the Fast Fourier Transform.