How should the amplitudes of spectral peaks of DTFT related?

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I was asked to plot using MATLAB, the magnitude of DTFT of

$$x(n) = 2cos(frac3pi 4n)+e^+jfracpi4n $$for n=0,1,2...100



It's been plotted and there are three peaks. (@ $frac3pi4$, $+fracpi4$, $-fracpi4$). plot of magnitude



The question is where I should expect spectral peaks and why (I know that the peaks occur at these frequencies but need to know how to explain).
Also I am to explain how the amplitude of those peaks should be related.




fourier-analysis




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  • Start expanding the cosine as sum of exponentials
    – N74
    Jul 15 at 8:44














up vote
0
down vote

favorite












I was asked to plot using MATLAB, the magnitude of DTFT of

$$x(n) = 2cos(frac3pi 4n)+e^+jfracpi4n $$for n=0,1,2...100



It's been plotted and there are three peaks. (@ $frac3pi4$, $+fracpi4$, $-fracpi4$). plot of magnitude



The question is where I should expect spectral peaks and why (I know that the peaks occur at these frequencies but need to know how to explain).
Also I am to explain how the amplitude of those peaks should be related.




fourier-analysis




share|cite|improve this question



















  • Start expanding the cosine as sum of exponentials
    – N74
    Jul 15 at 8:44












up vote
0
down vote

favorite









up vote
0
down vote

favorite











I was asked to plot using MATLAB, the magnitude of DTFT of

$$x(n) = 2cos(frac3pi 4n)+e^+jfracpi4n $$for n=0,1,2...100



It's been plotted and there are three peaks. (@ $frac3pi4$, $+fracpi4$, $-fracpi4$). plot of magnitude



The question is where I should expect spectral peaks and why (I know that the peaks occur at these frequencies but need to know how to explain).
Also I am to explain how the amplitude of those peaks should be related.




fourier-analysis




share|cite|improve this question











I was asked to plot using MATLAB, the magnitude of DTFT of

$$x(n) = 2cos(frac3pi 4n)+e^+jfracpi4n $$for n=0,1,2...100



It's been plotted and there are three peaks. (@ $frac3pi4$, $+fracpi4$, $-fracpi4$). plot of magnitude



The question is where I should expect spectral peaks and why (I know that the peaks occur at these frequencies but need to know how to explain).
Also I am to explain how the amplitude of those peaks should be related.





fourier-analysis





share|cite|improve this question










share|cite|improve this question




share|cite|improve this question









asked Jul 15 at 7:27









R SMITH

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  • Start expanding the cosine as sum of exponentials
    – N74
    Jul 15 at 8:44
















  • Start expanding the cosine as sum of exponentials
    – N74
    Jul 15 at 8:44















Start expanding the cosine as sum of exponentials
– N74
Jul 15 at 8:44




Start expanding the cosine as sum of exponentials
– N74
Jul 15 at 8:44















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