Work through Example 1 from Digital Filter Design by Zoran Milivojevi (Section 2.4.1.1). This will create a 10 th order FIR digital low-pass filter with

Work through Example 1 from Digital Filter Design by Zoran Milivojević (Section 2.4.1.1). This will create a 10^th order FIR digital low-pass filter with a cutoff frequency of 2.5 kHz for a sampling frequency of 20 kHz (use a rectangular window as in the textbook). Plot the normalized frequency response of the filter using the freqz() function in MATLAB. https://learn.mikroe.com/ebooks/digitalfilterdesign/

in here you click read and 2.4 examples

1. 
   

Note: freqz(b,a,n) generates an n point plot of frequency response of a digital filter with a transfer function defined by the coefficients in the arrays b and a (numerator and denominator coefficients, respectively). For an FIR filter, a = 1 (since there are no feedback coefficients). Use n = 1000 for a reasonably smooth frequency response plot.

1. Use the equations given in the text to generate coefficients for a 5^th order and 20^th order low pass filter with the same characteristics (once again, use a rectangular window). Plot their normalized frequency responses.
2. Generate coefficients for a 10^th order low pass filter with the same characteristics, but using a Hamming window this time. Plot its normalized frequency response.
3. Create an input signal x[n] consisting of the sum of a 100 Hz and a 10 kHz sine wave, both of amplitude 1. Remember to use a sampling frequency of 20 kHz (i.e. make sure you normalize both frequencies). Use each of the four digital filters you created previously to filter this signal, creating output signals y1[n], y2[n], y3[n], and y4[n], respectively. Plot the input signals and each of the output signals; clearly label each for easy identification.

Problem 2

1. More complex filters can be created as a sum or difference of two or more low pass filters. For example, an all-pass filter in the digital domain can be thought of as a low-pass filter with a cutoff frequency of π (the highest allowable frequency); a high-pass filter could be created by subtracting a low-pass filter with the desired cutoff frequency from the all-pass filter. Use this technique to generate coefficients for a 10^th order FIR high-pass filter with a cutoff frequency of 2.5 kHz for a sampling frequency of 20 kHz (use a Hamming window). Plot the normalized frequency response of the filter in MATLAB using the freqz() function.
2. Use the high-pass filter you just designed to filter the input signal, x[n], from Problem 1(d). Plot the output signal and compare it to the results from Problem 1(d).