Write a MATLAB function called convtd() to convolve a signal with a kernel in the time domain. It should have two input arguments: an input signal (a vector) and a kernel (also a vector). It will return the vector that results from the convolution, which should be the same length as the input signal.
Write a MATLAB function called convtd() to convolve a signal with a kernel in the time domain. It should have two input arguments: an input signal (a vector) and a kernel (also a vector). It will return the vector that results from the convolution, which should be the same length as the input signal.
The function will use a sliding window approach very similar to the bxcar() example from class.
The first thing you should do is validate your inputs. Make sure both are
Next, figure out the half-width of the kernel (the w variable in bxcar()).
You are now ready to write the loop in which you "slide" the moving window across the signal. As in bxcar(), leave the first and last w elements in the output set to 0. One way to compute the output signal sample for a particular position of the sliding window is to flip the order of the kernel coefficients (you can use the flip() function for this), multiply elements of the flipped kernel with the corresponding chunk of the input signal that is in the window, and then sum these products.
Write a script called testConvtd to test your function. This script should:
(1) Generate a kernel to implement a moving average filter 21 elements long--each element should be 1/21.
(2) Call your convtd() to filter a signal with this kernel. Download signal.dat from canvas to use as a test signal. This signal is sampled at 1 ms intervals (i.e., 1000 samples/sec).
(3) Plot the original signal and the filtered signal on the same axes in different colors.
(4) On another set of axes, plot the spectra of the original and filtered signals in different colors. You can use the periodogram() function for this as I've done in class. You can use the figure() command to open a new figure window.
(4) On a third set of axes, plot the frequency response of the kernel. Make sure the x-axis is in Hz
To turn in the assignment, upload convtd(), testConvtd, and your 3 plots. Save your plots as graphics files (e.g., jpeg). To get full credit, you must turn in all files and your code must be appropriately commented and indented.
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