How to use MATLAB Butterworth filtering

As far as I can tell, it doesn't seem like MATLAB has a dedicated notch filter function. The filter functions in Matalb are all regular analog and FIR and IIR filters. The notches in analog circuits tend to be double-T-shaped, which is achieved by phase cancellation.

I don't think the designers of MATLAB will be interested in these "weird tricks".

The formal approach is to use the band-stop filter function to implement it, and I won't talk about its advantages and disadvantages.

freqs() is to transfer data from the time domain to the frequency domain.

WA is your input.

b, a] are low-pass filter parameters.

h is the output.

The program is plotted in the form of 20*log10.

h = freqs(b, a, w) calculates the complex frequency domain response of the return filter based on the coefficient vector.

When calling this low-pass filter, use the following function.

sf=filter(a,b,s);s is the data to be filtered, and sf is the new data after passing through the low-pass filter you designed.

Digital or analog? RP is the passband ripple, and RS is the stopband attenuation, both of which are in dB.

Butterworth Bandpass Filter Design:

One. Request.

Center frequency: 40MHz

Upper passband limit: 42MHz; Lower limit: 38MHz

Bandwidth: 4MHz

In-band fluctuation AP <

Stopband attenuation: >60dB

Impedance: 50

Two. Design steps.

Known fda=42MHz, fdb=38MHz, BWD=, bandwidth=10%

1.Find the geometric center frequency first:

2.According to the formula, we can find kl, kc, and the bandwidth transformation constant ka

Where: fc=fb].

3.Select filter type: select CO5-10-27 from P37, A1-12where as=, ap=bandwidth: p=10%Meet the above conditions.

4.Find bw2, bw4

bw2 = 2 bwd [where 2 is found in p37, a1-12, CO5-10-27].

BW4 = 4 BWD [where 4 is found in P35, A1-12, CO5-10-27].

5.Find f2a, f2b, f4a, f4b, [2a], [2b], 4a], [4b].

6.Calculate the specific parameters of the circuit.

L1 = L1 ka kl (where L1 = C1 in CO5-10-27).

L2A = L2 ka KL [2A] (where L2 = C2 in CO5-10-27).

l2b=l2ˊ×ka×kl×[2b]

L3 = L3 ka kl (where L3 = C3 in CO5-10-27).

L4A = L4 ka Kl [4A] (where L4 = C4 in CO5-10-27).

l4b=l4ˊ×ka×kl×[4b]

l5=l5ˊ×ka×kl

Change the parameters yourself.

Let's make a program imitation with the filter prototype formula.

You've got a very high frequency bandpass filter, so let's do it with a waveguide.

Introduction Butterworth filter is a type of electronic filter. The Butterworth filter is characterized by the smoothest frequency response curve in the passband. This filter was first proposed by British engineer Stephen Butterworth in an article published in the British journal Radio Engineering in 1930.

Butterworth Filter CharacteristicsThe Butterworth filter is characterized by a flat frequency response curve in the pass band with no fluctuations, while the frequency response in the stop band gradually decreases to zero. On the wave diagram of the logarithmic diagonal frequency of the amplitude, starting from a certain boundary angular frequency, the amplitude gradually decreases with the increase of angular frequency, tending to negative infinity. The Butterworth low-pass filter is used to smooth the image disturbed by the noise.

Instance % by lyqmath

dlut school of mathematical sciences 2008

clc; clear all; close all;

i=imread('');

figure;

subplot(2, 2, 1); imshow(i); title('Original image');

j1 = imnoise(i, 'salt & pepper');Stacked salt and pepper noise.

subplot(2, 2, 2); imshow(j1); title('Add noise to the image');

g = fft2(double(j1));Fourier transform.

g = fftshift(g);Transform the data matrix.

m, n]=size(g);

nn = 2;% second-order butterworth low-pass filter.

d0 = 20;

m = fix(m/2);

n = fix(n/2);

for i = 1:m

for j = 1:n

d = sqrt((i-m)^2+(j-n)^2);

h = 1/(1+;Calculate the low-pass filter transfer function.

result(i,j) = h*g(i,j);

t(i, j) = h;

endend

result = ifftshift(result);

j2 = ifft2(result);

j3 = uint8(real(j2));

subplot(2, 2, 3); mesh(t); title('Schematic diagram of the filter')

box on;

Displays the filtered image.

subplot(2, 2, 4); imshow(j3); title('Filtering results'Results.

2 in WP 30 fs, that 30 is the passband cut-off frequency, and that one is changed to 2000, and the fs is a little larger than 4000.

See wp=2*30 fs?

30 is the cut-off stratosphere.

You're so awesome, I can't even read it.