First, find the Fourier Transform of the signal: f(x, y) = rect (x - 2/3) rect (
ID: 3885858 • Letter: F
Question
First, find the Fourier Transform of the signal: f(x, y) = rect (x - 2/3) rect (y + 1/2) Next, use MATLAB to make an image of f(x, y). For the x-y "window", image between -12 lessthanorequalto x lessthanorequalto 12 and -10 lessthanorequalto y lessthanorequalto 10. Use a sampling frequency f_s of 10 (step size of 0.1) in both directions. Next, use MATLAB to find the discrete Fourier Transform of f(x, y) (use fft2). Using the correct spatial frequencies (use freqvec.m if you like), image the magnitude of the fftshifted result. What happened to the spatial shift of the rects in the original space signal?Explanation / Answer
The Fourier Transform is extensively used in the field of Signal Processing. In fact, the Fourier Transform is probably the most important tool for analyzing signals in that entire field.
So what exactly is signal processing? I'll try to give a one paragraph high level overview.
A signal is any waveform (function of time). This could be anything in the real world - an electromagnetic wave, the voltage across a resistor versus time, the air pressure variance due to your speech (i.e. a sound wave), or the value of Apple Stock versus time. Signal Processing then, is the act of processing a signal to obtain more useful information, or to make the signal more useful.
How can a signal be made better? Suppose that you are listening to a recording, and there is a low-pitched hum in the background. By applying a low-frequency filter, we can eliminate the hum. Or suppose you have a digital photograph, and it is very noisy (that is, there are random specs of light everywhere). We can use signal processing and fourier transforms to filter out this undesirable "noise".
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