2 DTFT Properties (a) Use the definition of the DTFT to derive a symmetry property: if rn] is real-valued, then X(e)is conjugate symmetric about the origin. b) Use the definition of the inverse DTFT to derive a symmetry property: if X(e) is real-valued and an even function, then r[n] is real-valued and an even function, (c) Given the two sampled data signals rn] and hin], sin (즉n sin (^n) rfn] and hn Find the convolution, y[n]-Σ00-00 hkjz[n-k]. Hint: think more,...
Please help with the following continuous and discreet problem! Thanks! 6. Using the definition compute the inverse DTFT for the following signal (2m + 1)π NE 6. Using the definition compute the inverse DTFT for the following signal (2m + 1)π NE
Problem 1: Find Xo),the DTFT of sinlFndi' Z transfomn and DTFT. Plot its amplitude frequency spectrum for-π<ω<π. What is the period of X(o)?
Why do we need DFT in addition to DTFT? What is the difference between DTFT and DFT? The frequency-domain sampling is equivalent to the time-domain ( What is the minimal condition of digital samples of your signal in order to use FI
1. Find the DTFT of the sequence x[n] = 0.5%u[n] . Express the DTFT in magnitude-phase form.
6. Let X(e2) be the DTFT of a signal nl which is known to be zero for n < 0 and n > 3. We know X(eim) for four values of N as follows X (ejm)0, X(en/2) X(eT/2)5 5j, X(ej0) 10, 55j = = = (a) Find n. (Hint: Compute the IDFT) (b) Find X(ei?)
Lab #2 Discrete-time Fourier Transform (DTFT) OBJECTIVES: • Explore the DTFT, its meanings and concepts. • Get acquainted with Matlab/Octave 1) Start MATLAB and change the “Current Directory” in the top of the window (or type) >> cd '' (example: >> cd 'C:\NIU\lab2') Alternatively, if you don't want to use MATLAB, you can open a web-browser and go to “octave-online.net”. 2) Download and execute LAB2forStudent_A.M with >> lab2forStudent_A and observe that it produces a Discrete-Time (DT) signal xVec. 3) TO...
Consider the signal f[k] illustrated below 3 2 1 (a) Using the definition, provide the DTFT of flk]. (b) Express f [kas a rect function. Use the DTFT pair to solve for the DTFT (it should look a lot different from the previous solution) c) Verify that both of your solutions are, in actuality, the same by evaluating them at 0, T/2, T Consider the signal f[k] illustrated below 3 2 1 (a) Using the definition, provide the DTFT of...
4. Derive the Maclaurin series for In (1 + x) 5. Derive the Maclaurin series for In (1 – x) 6. Derive the Maclaurin series for In (*) 7. Find the Maclaurin series for x sin x (1-x)
1. The condition for signal x[n] to have DTFT is that x[n] is: (a) integratable, (b) differentiable, (c) summable, (d) compressible. 2. If X(92) is the DTFT of x[n], then the Fourier transform of x[-n) is (a) X(92)ej, (b) X(22)ein (c) X(32-1), (d) X(-22) 3. For 8-point computation of DFT, how many complex multiplications are involved? (a) 8, (b) 16, (c) 32, (d) 64. 4. For 32-point computation of FFT, how many complex multiplications are involved? (a) 32, (a) 325...