MATLAB signal processing [Q & A essays · 2]

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