how linear fir algorithm works?

function [y,z] = fir_filt_linear_buff(b,x,z)
    y = zeros(size(x));
    for n=1:length(x)
        z = [x(n); z(1:end-1)];
        y(n) = b * z;
    end
end

in this why z is used?

i dont understand the need to use z.

please help

Answer 1

[Prabhan Purwar]

Hi,

hope this example is leveraged from the following link:

• https://in.mathworks.com/help/fixedpoint/examples/implement-fir-filter-algorithm-for-floating-point-and-fixed-point-types-using-cast-and-zeros.html

The following function represents an FIR filter with a linear buffer, where b is a row vector and z is a column vector the same length as b. x represents the input signal, b represents the filter coefficients and z represents delay/buffer in the signal.

For example:

x=[1 2 3 4 5]; % Signal
b=[1 1 1 1 1]; % Filter Coefficients, kept as unity to demonstrate effect of z
z=[0 0 0 1 0]'; % Delay/buffer 
y = zeros(size(x));
    for n=1:length(x)
        z = [x(n); z(1:end-1)];
        y(n) = b * z
    end

If z=[0 0 0 0 0]' (No delay) y=[1 3 6 10 15] (FIR Output) as expected

If z=[0 0 0 1 0]' (Delay of 1 at 4th col) y=[2 3 6 10 15]

If z=[0 0 1 0 0]' (Delay of 1 at 3rd col) y=[2 4 6 10 15]

if z=[0 1 0 0 0]' (Delay of 1 at 2nd col) y=[2 4 7 10 15]

if z=[1 0 0 0 0]' (Delay of 1 at 1st col) y=[2 4 7 11 15]

For more details refer to the FIR Filter Structures.

Hope it helps!!