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MATLAB signal processing [Q & A essays · 2]
2022-07-07 23:21:00 【Goose feather is on the way】
1. Matlab Simple interpolation 、 Fitting method
answer :
clc,clear,close all;
x = linspace(-2,2,10);
y = exp(-x.^2);
figure(1)
stem(x,y,"LineWidth",1.5)
grid on
title('f(x)')
%interp1 linear interpolation
xq = linspace(-2,2,20);
vq1 = interp1(x,y,xq);
figure(2)
plot(x,y,'o',xq,vq1,':.',"LineWidth",1.5);
xlim([-2 2]);
grid on
title('interp1 linear interpolation ');
%polyfit Polynomial fitting interpolation
p = polyfit(x,y,7);
y1 = polyval(p,x);
figure(3)
plot(x,y,'g-o',"LineWidth",1.5)
hold on
plot(x,y1,"LineWidth",1.5)
hold off
xlim([-2 2]);
grid on
title('polyfit Polynomial fitting interpolation ');
%spline Cubic spline interpolation
yy = spline(x,y,xq);
figure(4)
plot(x,y,'o',xq,yy,"LineWidth",1.5)
xlim([-2 2]);
grid on
title('spline Cubic spline interpolation ');
2. Digital signal processing experiment ——FIR Filter design
ask : It is known that the input signal is a signal mixed with noise
x(t)=sin(250πt)+cos(500πt)+cos(700πt)
① Draw the time domain waveform and spectrum diagram of the input signal , And point out the frequency components it contains ( With Hz In units of );
② Assume that the intermediate frequency component of the input signal is a noise signal , How to design a digital filter to process the mixed signal , Give reasonable design indicators and explain the reasons , Draw the frequency response characteristics of the filter : More than two implementation schemes are required .
③ use (2) The filter designed in completes filtering and verifies the design scheme , Draw the time domain waveform and spectrum of the filter output signal .
answer :
clc,clear,close all;
t = -0.08:0.0001:0.08;
n = -100:100;
L = length(n);
fs = 1000;
x0 = sin(2*pi*125.*n/fs); % Time domain sampled signal t=nT=n/fs
x1 = cos(2*pi*250.*n/fs);
x2 = cos(2*pi*350.*n/fs);
x3 = x0 + x1 + x2;
% Time domain signal
figure(1)
subplot(411)
plot(t,sin(2*pi*125.*t),"LineWidth",1.5)
grid on
subplot(412)
plot(t,cos(2*pi*250.*t),"LineWidth",1.5)
grid on
subplot(413)
plot(t,cos(2*pi*350.*t),"LineWidth",1.5)
grid on
subplot(414)
plot(t,sin(2*pi*125.*t)+cos(2*pi*250.*t)+cos(2*pi*350.*t),"LineWidth",1.5)
grid on
% Filter design
wn = 3/5; % Cut off frequency wn by 3/5pi(300Hz),wn = 2pi*f/fs
N = 60; % Order selection
hn = fir1(N-1,wn,boxcar(N)); %10 rank FIR low pass filter
figure(2)
freqz(hn,1);
figure(3)
y = fftfilt(hn,x3); % after FIR The signal obtained after the filter
plot(n,y,"LineWidth",1.5)
grid on
% Spectrum analysis
X = fft(x3); % Unfiltered spectrum
p2 = abs(X/L);
p1 = p2(1:L/2+1);
p1(2:end-1) = 2*p1(2:end-1);
Y = fft(y); % Of the output signal fft
P2 = abs(Y/L);
P1 = P2(1:L/2+1);
P1(2:end-1) = 2*P1(2:end-1);
f = fs*(0:(L/2))/L;
figure(4)
subplot(211)
plot(f,p1,"LineWidth",1.5)
title('Single-Sided Amplitude Spectrum of X(t)')
xlabel('f (Hz)')
ylabel('|p1(f)|')
grid on
subplot(212)
plot(f,P1,"LineWidth",1.5)
title('Single-Sided Amplitude Spectrum of Y(t)')
xlabel('f (Hz)')
ylabel('|P1(f)|')
grid on
Time domain waveform : Respectively 125(2pi*125=250pi)、250 and 350Hz Cosine signal
The cut-off frequency is 300Hz Of FIR low pass filter :
Spectrum before and after filtering :
Filtered time domain signal :
3. Matlab Why is the heat map not a smooth transition ?—— Pseudo color map function pcolor() Usage of
Problem related code :
clear; clc; close all
[,,raw ] = xlsread(' Heat map data of sports facilities .xlsx');
mat = cell2mat(raw(2:end, 2:end));
imagesc(mat); % Generate heat map
c=colorbar;
colormap hot;
ylabel(c,'Population Heat');
caxis([1 11]) % Change the maximum and minimum values of the right color bar
xticks(1:13) %x Axis Division 13 Equal division
xticklabels(raw(1,2:end))
yticks(1:15)
yticklabels(raw(2:end,1))
Expected effect :
answer : It may be the reason for the small amount of data , The expected effect is not just for use imagesc(), It is more like a pseudo color image after color interpolation , Suggested attempt pcolor():
clc,clear,close all;
data=round(rand(1,900)*100);
data=reshape(data,10,90);
h=pcolor(data);
h.FaceColor = 'interp';
set(h,'LineStyle','none');
clc,clear,close all;
data=round(rand(1,900)*100);
data=reshape(data,10,90);
h=pcolor(data);
h.FaceColor = 'interp';
colormap jet;
colorbar;
set(h,'LineStyle','none');
Pseudo color map function pcolor() Usage of :pcolor Official documents
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