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

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

Answer 1

[Wayne King]

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);

[Ben]

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)

Answer 2

[Wayne King]

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.

[Ben]

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