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implementing a "first difference" filter in Matlab defined by a difference equation.

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Ben
Ben 2013-10-24
评论： Ben 2013-10-24
Hi all
I am a student in a digital signal processing module and I am stuck on the final question of a lab session and I am not sure if my understanding is correct, i have already tried asking the lab tutor for help via email but no reply (he's a PHD candidate). the difference equation is shown below.
y[n] = x[n] - x[n -1]
He tells us its simple and can be achieved with one line of code.
My code is shown below, my understanding is its a second order difference equation.
FD = repmat(1/2,1,2); %repmat creates large matrix of 1 row by 2 columns (every coefficient value 1/2=0.5) FD_Filtered = firfilt(FD, x); %filtering input signal x with FD filter
Any advice will be greatly appreciated.
Thanks in advance,
Ben

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回答（2 个）

Wayne King
Wayne King 2013-10-24
No, I just mean filter(). A causal N-point moving average filter just has filter coefficients of 1/N
b = 1/N*ones(N,1);
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Ben
Ben 2013-10-24
编辑：Ben 2013-10-24
Ok thanks I understand now that this has two 1 and -1 right hence the y[n] = (1/1)x[n] + (1/-1)x[n-1] = x[n]-x[n-1]
therefore FD = [1 -1] (filter coefficients)

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Wayne King
Wayne King 2013-10-24
Why do you believe it's a second order difference equation?
Since it is a homework problem, I do not want to simply give you the answer, but look at filter()
He is correct in telling you that you can do it easily with one line of code.
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Ben
Ben 2013-10-24
the previous questions were to design moving average filters which were defined by a summation equation example;
y[n]= 1/5 ∑_(k=0)^4▒〖x[n-k]〗 (k going from 0 to 4 (4 = M-1) M=5)
for 5 point average so can the difference equation in the question be shown a similar way;
y[n]= 1/2 ∑_(k=0)^1▒〖x[n-k]〗 (k going from 0 to 1 when M-1=1 and M=2)
Do the filter coefficients seem correct?
By look at filter() do you mean firfilt()?
Thanks for advising

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