Questions tagged [dtft]

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frequency spectrum of a sampled signal, PSD and power discussion

Before I go into my question, I first want to review the basics of sampling a signal and at the same time I build the basics of my questions so that they make more sense. I know I have asked couple of ...
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17 views

Characterizing a non-LTI system

How should we characterize a non-LTI system? For example we have: $y[n]=x[3n]+x[2n]+x[n]$ which is clearly not LTI. Also, the impulse response will be $h[n]=3\delta[n]$ and if we take the DTFT of this ...
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37 views

What is the formula for the frequency spectrum?

A signal $f[n]$ is given, the corresponding DTFT as $F(e^{j\omega})$ and a plot of the frequency spectrum $f(t)$. Unfortunately I can't find a formula for the frequency spectrum in my documents. When ...
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32 views

Orthogonality of filter impulse response to its even shift

I meet this problem but still do not know how to solve it. Could you guy give me some guides? Upsampling by 2 ($U_2$) followed by filtering by $g$, with operator $G$ And given: $<g_n,g_{n-2k}>...
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39 views

DTFT of window function applied to input signal

$$x[n] = cos(\omega_1n) + cos(\omega_2n)$$ $w[n] = 1/N$ for $0 \leq n < N, 0$ for everything else Find the DTFT of $y[n]=x[n]w[n]$ expressed by the DTFT of $w[n]$, $W(\omega)$ I was thinking ...
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42 views

z-transform and DTFT properties

I actually do not understand what to do with the third property of the impulse response g[n] and how it has to be determined. Thanks in advance!
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39 views

IFFT, negative frequencies and noncausal impulse

When using the IFFT to compute an approximation to the IDTFT, frequency range is 0 to 2$\pi$ versus $-\pi$ to $\pi$. This produces a different impulse sequence(causal I think). How do you calculate ...
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1answer
103 views

Matlab FFT not producing symmetric spectrum

I am plotting a FFT of a sampled RC pulse but my resulting spectrum isn't symmetric - it's offset. ...
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1answer
85 views

Calculating DTFT

When calculating DTFT of (1/2)^n u[n]. We evaluate the sum as follows: Please correct statements and answer questions below: 1) So to go from STEP 1 to STEP 2, the limits of the series are changed ...
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93 views

DTFT of $ f[k] = 3^k u(-k-1)$

Find the Discrete-time Fourier transform of $ f[k] = 3^k u(-k-1)$ (then sketch it and find its magnitude & angle). It doesn't fit any templates on the Fourier table, and I don't see how one ...
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112 views

Confusion in understanding the Proof of DTFT

While understanding the proof of DTFT from Signals and Systems by Oppenheim, I have confusion in understanding few steps. $$ x'[n]=\sum_ {k=<N>} a_ke^{jk(2\pi/N)n}$$ $$ a_k= \frac{1}{N} \sum_ {...
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53 views

DTFT inconsistency

Let $x[n] = u[n] - u[n-4]$ (a discrete pulse of length 4), and $X(\omega)$ is its DTFT. Let $x_1[n] = x[n]*x[n]$. I expect DTFT of $x_1[n]$ to be same as $X(\omega)$, because $x_1[n]$ has the same ...