MATLAB: A help with fourier transform

convolutionfouriernon-matlab questionsinc

can any one help me with this question please ?

the question says: using fourier transform properties, prove that sinc(t)*sinc(t) = sinc(t)

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Assuming your * means convolution, which is often two *, and knowing that convolution in one domain is multiplication in the other domain:

fft(sinc**sinc) = fft(sinc) * fft(sinc) = rect*rect = rect

and

ifft(rect) = sinc = same as what you started with.

so sinc**sinc = sinc.

Related Solutions

MATLAB: Accessing sinc(0) using the Symbolic Math Toolbox.

The Symbolic Toolbox does not define a sinc() function. You are getting the purely numeric sinc() function from the signal processing toolbox. That function works by testing the input for 0 using logical indexing. Unfortunately when you pass in a symbolic variable, that is not equal to 0 (because it is a symbol, not 0), so no special handling is arranged for that case.

You will have to program around this.

You would not be able to use piecewise() even if you had R2016b, because symfun() cannot generate code for piecewise().

You will need to reconsider using sinc() in a symbolic function. For example, define

syms SINC(t)

and code in terms of SINC(t) without having defined SINC(t) anywhere. Call matlabFunction. You will get a warning about unknown function SINC, but it will be written into the handle. Then you bring SINC.m onto your path, defined as

function y = SINC(x)
  y = sinc(x);

Now that is done, you can run the anonymous function you generated.

If your had SINC.m on the path at the time you did the matlabFunction, it would have called the function with the symbolic expression as parameter, leading to sin(t)/t being generated right in the code. But with SINC.m not on the path at the time of the matlabFunction, it just generates the name in the function handle, and then when you put it on the path and run the function handle it will find the SINC.m

MATLAB: Ringing effect in time domain reconstructed signal after filtering

Not sure exactly what you did, but in general, in Linear Systems Theory (Fourier Filtering), multiplication in one domain is equivalent to convolution in the other domain. A band pass filter is a rect function and the Fourier Transform of a rect function is a sinc function. So when you multiply by a rect function in the Fourier domain to do band pass filtering, it's like you convolve with a sinc function in the time domain. Since the sinc function has ripples, so will your output signal. Yes this is the Gibbs phenomenon. And since wider in one domain means narrower in the other domain, a wider rect will give a narrow sinc (faster ripples) while a narrow rect will give a wider sinc and slower ripples.

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Related Solutions

MATLAB: Accessing sinc(0) using the Symbolic Math Toolbox.

MATLAB: Ringing effect in time domain reconstructed signal after filtering

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