扫频/啁啾信号以不正确的频率结束

Question

我正在使用matlab / octave创建一个扫描/啁啾信号，我的结束信号似乎以错误的频率结束。如何修复它以使信号以正确的频率结束。

PS：我不能在八度音阶中使用chirp命令，因为我正在使用特定的等式创建一个啁啾/扫描信号。

使用简单等式的示例代码。和问题的情节

%test sweep / chirp

clear all,clc
freq1=20; %start freq
freq2=200; %end freq
fs=44100;
dur=1; %duration of signal in seconds

t = linspace(0,2*pi,fs*dur);

f=freq1:(freq2-freq1)/length(t):freq2-(freq2-freq1)/length(t); 
%20:(200-20)/lenght(t) :200-(200-20)/length(t)

data=sin(f.*t); %build signal
data=(data/max(abs(data))*.8); %normalize signal
wavwrite([data'] ,fs,32,strcat('/tmp/del.wav')); %export file
plot(t,data)

PS：我正在使用八度音阶3.8.1

Answer 1

以下代码说明了如何生成频率可变的正弦波。

freq1=20; %start freq
freq2=200; %end freq
dur=1; %duration of signal in seconds


freq=@(t)freq1+(freq2-freq1)/dur*t;
%another example, may help to understand the code
%dur=2
%freq=@(t)heaviside(t-1)*10+heaviside(t-1.5)*-9;
%Integerate over the time-local frequency, gives the average frequency until t which later on gives the sin with the right phase
%In case you don't have symbolic toolbox, integrate manually. For the given numbers Ifreq=@(x)x.*(x.*9.0+2.0)
Ifreq=matlabFunction(int(freq(sym('x'))));
%Defining wave function based on `Ifreq`
wave=@(t)(sin(Ifreq(t)*2*pi));
t=0:.00001:dur;
plot(t,wave(t));

Answer 2

在Daniel's recipe之后，这是一个使用数值积分的版本，因此不需要符号工具箱：

freq1 = 20;  % start frequency
freq2 = 200; % end frequency
fs = 44100;
dur = 1;     % duration of signal in seconds

t = 0:1/fs:dur;
freqt = linspace(freq1,freq2,numel(t));
ifreqt = cumsum(freqt)/fs;
data = sin(2*pi*ifreqt);
plot(t,data);