Question

A discrete- time system has the following unit- pulse response:h[n] = 0.3(0.7)ⁿu[n] Use Conv in matlab to calculate the response of this system to x[n]=u[n], and plot the response.

Answer 1

The student's question pertains to calculating and plotting the response of a discrete-time system with a known unit-pulse response to a unit step input using MATLAB's conv function. The provided MATLAB code illustrates how to perform the convolution and generate a plot of the system's response.

Step-by-step explanation:

The question deals with a discrete-time system and its response to a unit step input. In this scenario, the system has a given unit-pulse response h[n] = 0.3(0.7)ⁿᵉ[n], where u[n] indicates the unit step function that is active for n ≥0. The input to the system is x[n] = u[n], which is also a unit step function. To find the system's response to x[n], convolution operation in MATLAB can be used, represented by the conv function.

The MATLAB code snippet for the convolution and plotting of the response would look like this:

n = 0:100; // Define a range for n
h = 0.3 * (0.7).^n; // Define the unit-pulse response
x = ones(1, length(n)); // Define the step input
y = conv(h, x); // Convolve input and impulse response
stem(0:length(y)-1, y); // Plot the response
title('System Response to Step Input'); // Title of the plot
xlabel('n'); // Label for x-axis
ylabel('Response'); // Label for y-axis

This MATLAB code generates the output signal y[n] which is the convolution of h[n] and x[n], and it plots the resulting system response over a discrete-time range.