Question

can someone please help me with this, I'm really stuck.

here a sample code provide for the matlab:

clear all; close all;
% ---------- (a) ----------

a = 0.7; % attenuation coef.
D = 5; % digital time delay
UnitImpulse = [1 zeros(1,???)]; % creat unit impulse, starting from n=0;
x = UnitImpulse;
y = filter(1, [1 zeros(1, D-1) -a], x); % help filter, do you know the usage of filter() now?
n = 0:(length(y)-1); % check length of y[n]
figure
stem(n, y); % is it the same as that in your derivation?
xlabel('n')
title('Impulse response')

% ---------- (b) ----------
% Please comment whether this reverberator can be potentially implemented in real time and under what condition of a and D this reverberator is stable.

ComputerHW2 Spring2019.pdf - Adobe Acrobat Reader DC 檔案(F) 編輯(E) 檢視(V) 視窗(W) 說朗(H) 首頁 工具 EE2020_homew... ComputerHW2...X Topic1_SignalsA... Topic1_Signals.A.. Topic1_Signal. Topic2_LTISyst... Topic2_LTISyste... 登入 山共用 will try to implement and tune this digital recursive IIR reverberator which is modeled as follows where all the symbols in the LCCDE share the same definitions as we discussed in the class. With this LCCDE modeling, please try to answer the following questions (a) Derive the impulse response of this reverberator, and then use the MATLAB function filter0 to compute and plot the impulse responses of this reverberator to 0.7, and D-5 (b) Please comment whether this reverberator can be potentially implemented in real time and under what condition of a and D this reverberator is stable. Prove them. 0 verify your derivation , where a 2 (c) Approximate the this reverberator by a FIR system and implement it using the MATLAB function conv0 with a = 0.7 and D= tFs where D is an integer representing the digital time delay given the continuous-time delay τ= 0.1 sec and sampling rate Fs (in Hz). Given the sound file Halleluyah.wav, you can load the file, play the sound and save the output sound by using the following I> MATLAB co

Answer 1

Modified executable matlab code is given below.

clear all; close all;
% ---------- (a) ----------

a = 0.7; % attenuation coef.
D = 5; % digital time delay
UnitImpulse = [1 zeros(1,100)]; % creat unit impulse, starting from n=0;
x = UnitImpulse;
y = filter(1, [1 zeros(1, D-1) -a], x); % help filter, do you know the usage of filter() now?
n = 0:(length(y)-1); % check length of y[n]
figure
stem(n, y); % is it the same as that in your derivation?
xlabel('n');grid on;
title('Impulse response');

RESULT:

The impulse response is sketched below for a = 1.7 and D = 5

Impulse response 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0 10 20 30 4050 60 70 80 90100

The system will go unstable for |a| > 1 because the region of convergence does not contain the unit circle.

For the case of a = 1.5 and D = 5, the impulse response is sketched below.

Impulse response 3500 3000 2500 2000 1500 1000 500 0 0 10 20 30 4050 60 70 80 90100

It is observed that the impulse response is exponentially increasing that makes the system unstable.

For any positive values of D, the system is stable, considering |a| < 1.

% ---------- (b) ----------

The reverberator can be potentially implemented in real time and for |a|<1 and for any value finite value of D and the reverberator is stable