1. Suppose length-4 discrete-time signalan) and h(n) have discrete Fourier transforms X and H. Xx =...
The discrete Fourier transform of an mxn matrix X = (Xj.k) is an m x n matrix X = (ĉik) m,n ypj yqk pqSm Sn, p.q=1 where Šm = e270i/m The corresponding inverse Fourier transform is m.n Xj,k = (mn)-1 » počinje-k. p, Sm Sn . peq=1 Let X and Y be mxn matrices with the discrete Fourier transforms X and Y respectively. Define two dimensional circular convolution Z = X * Y to be min Za,b = XXj,kYa–j,b-k j,k=1...
2TT sinn (1) a) Let x1 [n] = πη Find the Discrete Time Fourier transform of this signal and plot it with all its critical values. (you can use only transform tables from the book). b) Now, define xzlv) = (**) GHS) Using transform properties, find the Discrete Time Fourier transform of x2[n] and plot it with all its critical values. In your calculations be sure to show your steps ! 2TT sinn sinn sinwon c) Let y[n] [( )...
Problem 3: Let x(n) be an arbitrary signal, not necessarily real valued, with Fourier transform X (w). Express the Fourier transforms of the following signals in terms of X() (C) y(n) = x(n)-x(n-1) (d) v(n) -00x(k) (e) y(n)=x(2n) (f) y n even n odd , x(n/2), (n) 0 Problem 4: etermine the signal x(n) if its Fourier transform is as given in Fig. P4.12. X(a) 0 10 10 10 X(o) 0 X(a) Figure P4.12 Problem 3: Let x(n) be an...
Consider the discrete time signal x[n]: 13 -5 10 2.5 Compute the discrete time Fourier transform (DTFT) X (A). Find the period ofX(Q). Hint: First write the x[n] showed above as two pulse functions then take the DTFT using the equation given below Express discrete Fourier transform (DFT) of x[n] using DTFT X(Q). a. b. Consider the discrete time signal x[n]: 13 -5 10 2.5 Compute the discrete time Fourier transform (DTFT) X (A). Find the period ofX(Q). Hint: First...
Explain how fourier transform is done? 1. (8 points) Suppose a particular discrete-time linear and time-invariant (LTI) system has frequency response H(e) and that when its input is z[n] = 2 cos (n). the corresponding output is y[n] = 6 cos (n+ ) Find the real part and imaginary part of H(e)") at w = .
DSP 4. (12 points) (a) (4 points) Let x[n] = {1,2, 1, 2} and h[n] = {1,-1,1, -1} be two length-4 sequences defined for 0 <n<3. Determine the circular convolution of length-4 y[n] = x[n] 4 hin). (b) (6 points) Find the 4-point discrete Fourier transform (DFT) X[k], H[k], and Y[k]. (c) (2 points) Find the 4-point inverse DFT (IDFT) of Z[k] = {X[k]H[k].
(a) Consider a discrete-time signal v[n] satisfying vn0 except if n is a multiple of some fixed integer N. i.e oln] -0, otherwise where m is an integer. Denote its discrete-time Fourier transform by V(eJ"). Define y[nl-v[Nn] Express Y(e) as a function of V(e). Hint : If confused, start with N-2 (b) Consider the discrete-time signal r[n] with discrete-time Fourier transform X(e). Now, let z[n] be formed by inserting two zeroes between any two samples of x[n]. Give a formula...
roblem 3: (15-7+8 points) Consider the left-sided discrete-time signal a(n)42+1). a) Find the discrete Fourier transform X(eju n-2 ). (b) Find the phase (o) of the discrete Fourier transform X
Please solve using the Discrete-Time Fourier Transform: Given a filter described by the difference equation y[n] = x[n] + 2x[n - 1] + x[n - 3] where x[n] is the input signal and y[n] is the output signal. a) Find H[n] the impulse response of the filter. b) Plot the impulse response c) Find the value of H( Ω) for the following values of Ω = 0, pi, pi/2, and pi/4
1. Using appropriate properties and the table of Fourier transforms, obtain and sketch the sin(at) Fourier transform of the signal x()cn(31-4 marks) 2fX(a), determine the Fourier transform of the signal y(t)dx( F.T. dx(2t) dt (3 marks) 3. Find the Fourier transform of x(t)-cos(2t/4). (3 marks) 4. Let x(t) be the input to a linear time-invariant system. The observed output is y(t) 4x(t 2). Find the transfer function H() of the system. Hence, obtain and sketch the unit-impulse response h(t) of...