# DTFT

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Having problems working out DTFT properly. Attached is 5 problems. Request assistance with these and if possible short narrative to each step to help me understand better.

1. Compute the DTFT of the discrete-time signal shown in the Figure below.

2. For a discrete-time signal x[n] with the DTFT where b is an arbitrary constant compute the DTFT V(Ω) of v[n] = x[n] - x[n-1]

3. Compute the inverse DTFT of X(ω)=cos2Ω

4. Compute the inverse DTFT of: X(ω)=sinΩ cosΩ

5. Compute the rectangular form of the four-point DFT of the following signal, which is zero for n<0 and n>=4.

x[0]=1, x[1]=-1, x[2]=1, x[3]=-1

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1. Compute the DTFT of the discrete-time signal shown in the Figure below.

Solution: The discrete signal can be represented below:

To get the discrete-time Fourier transform (DTFT) X(Ω), we'll use the formula:

Now, let's get the summation by substituting the values:

Using the geometric series equation, we have:

Simplifying, we have the final answer of:

...

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