You shouldĮxperiment with the NFFT variable to get the best result.Problem 1 Problem 2 Problem 3 Problem 4 Problem 5 Problem 6Īdd your Rhea contribution to the Course-Related_Material pageĪdam has posted some Helpful Youtube videos which will be very helpful in working this problem.
Prepare a set of plots to explain to the TA how you solved this problem.įrom part (a) by taking a spectrogram of the touchtone signal. Make sure you clearly and neatly present your results. (All of these commands are in theįilters to determine the phone number in touchtone.wav. Load the sequence into your computerĪnd play it. This is called the DTMF (Dual-Tone Multiple-Frequency) "9", you generate a tone that is the sum of a 1477 Hz sine waveĪnd a 852 Hz sine wave because "9" is at the intersection of that Press a button you generate a tone that is the sum of the column frequencyĪnd the row frequency. The picture below shows a typical touch-tone phone pad. The sinusoidal signal to act as a bandpass system? Only a significant output around t=2 seconds, when the frequency of the chirp The signal (f400) behaves as a bandpass filter - there is %"n" so we can plot just the beginning part of z. %Because z is longer than y, create a new vector (All of theseĬommands are in the file Lab7_matlab_code.m).į400=sin(2*pi*400*t1).*exp(-40*t1) %A 400 Hz decaying sine wave. (note that the maximum frequency on the spectrogram is 4000 Hz because theĬreate a short sinusoidal signal (1/10 second) at 400 Hz, andĬonvolve it with the chirp. You can visualize the increasing frequency with a spectrogram These commands are in the file Lab7_matlab_code.m). (i.e., the frequency increases at 200 Hz/sec). (All of Note: Compare your results with the convolutions on the web site to make sure you have correctly scaled the convolution sum.Ĭreate a chirp signal that goes from 0 to 2 kHz in 10 seconds
Introduce an appropriate vector of time values so that the horizontal axis of your plot is correct. Then, perform the continuous-time convolutions using 'conv' and plot the result. Letting T=0.01, create vectors representing the three continuous-time signals on the "Joy of Convolution" web site, starting at t = 0 for each signal. Therefore, the sum must be multiplied by T to reflect the width of the sampling interval. The convolution integral can then be approximated by thinking of the sum performed by 'conv' as a Riemann sum. Create two new additional signals of your choice for x and h to test and demonstrate your convolution of arbitrarily shifted functions.Ĭ) Now look at the examples of continuous-time convolution at the "Joy of Convolution" web site To use 'conv' for continuous-time signals, the vectors representing the continuous-time signals are the values of the signals sampled at some period T. Then running the m-file will make the three plots. To run this m-file, you will first set x and h to one of the three vectors of values from part (a), and assign values to nx and nh. Write an m-file that plots x, h, and conv(x,h) with the correct time indices. (Since MATLAB always starts vector indices at 1, you will have to introduce a separate vector for the values of n.)ī) Suppose the signals in part (a) are shifted in time so that the first non-zero value of the signal x starts at nx and the first nonzero value of h is nh, where nx and nh are arbitrary integers. Plot your results with the correct values of n on the horizontal axis. Define your signals in an m-file, or save them so that you can reload them so that you can show the TA your work. To become familiar with this command, use it to compute some of the convolutions for the discrete-time signals on the "Joy of Convolution" web site To do this, create vectors representing the three discrete-time signals (beginning at n=0, the first non-zero value for each signal), and compute the convolutions using the 'conv' command. A) The MATLAB command 'conv' computes the convolution of two vectors.