MATLAB: Use modified covariance (MC) method to estimate frquency

frequency estimatemc estimator

let x(t)=10cos(200*pi*t+1.2) which is a continuous-time sinusoid. The x(t) is sampled every Ts=0.001 sec. to obtain a sequence x[n] where x[n]=x(nTs) for n between 0 and 100 (including 0 and 100)
how can I use modified covariance (MC) method, given the following code, to determine the frquency estimate for x[n].
 function w = mc(x);
 % w = mc(x) is used to estimate frequency
 % the MC method from the vector x
 % x is supposed to be a noisy single-tone sequence
 % w is the estimated frequency in radian
 N=max(size(x));
 t1=0;
 t2=0;
 for n=3:N
 t1=t1+x(n-1)*(x(n)+x(n-2));
 t2=t2+2*(x(n-1))^2;
 end
 r = t1/t2;
 if (r>1)
 r=1;
 end
 if (r<-1)
 r=-1;
 end
 w=acos(r);
btw, What is purpose of setting r to 1 and -1 when its value is larger than 1 and smaller than -1,respectively?
thank u in advance.

Best Answer

I'm not familiar with this algorithm for frequency estimation. When I use the term "modified covariance method", it's in the context of autoregressive spectral estimation, but having said that it seems to work here.
 t = 0:0.001:0.1-0.001;
 x = 10*cos(200*pi*t+1.2); %although this signal is not corrupted by noise
 w = mc(x);
returns 0.6283 radians/sample, that is equivalent to 628.3 radians/second which is 100 Hz (the frequency of the input sinusoid in cycles/second).
To answer your final question, the real-valued cosine function takes values between [-1,1]. If you take the inverse cosine of values in the interval [-1,1], you will get a real-valued output. However, if you take the inverse cosine of a value larger than 1, or smaller than -1, you will get a complex-valued output. The complex-valued cosine is not bounded by 1.
The code is ensuring that you do not input any values to acos() outside the interval [-1,1], so that the output is real-valued.
To use the function, mc.m, save the file in a folder on the MATLAB path and you can run it from the command line. For example, if you have the file in a folder called c:\mfiles, use
>>addpath 'c:\mfiles'
to add that folder. or you can use
>>pathtool
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