how to design Filters using verilog and nios? like butterworth, high and low pass etc

Basically what you need is rather to calculate the filter parameters and normalize them for integers. Or that is what I have done in the past. Filters are basically additions of different "volumes" over a length of time. The Code itself is not the hard part. But what I tend to do for simple filters is to simulate an ordinary RC filter like this out<=out+(k*(in-out)/256) ... K being 0-256 here.. this also works with resonance and feedback if you limit the signals and what not. Interpolation uses the same formula but with different inputs/outputs.

    reg signed yaudio ;  //yaudio is output from filters (audioout is input)
    reg signed ac;    //accumulator
    always @ (posedge clk30)
    begin
    reg signed b0=68; //lowpass filter response
    reg signed b1=16;
    reg signed b2=68; //(or 76) ,b2 is most often same as b0(could be optimized)
    reg signed a1=117;
    reg signed a2=-54;
    reg signed in;
    reg signed wa,wb,wc;
    reg  l;        //timer limit value
    reg  co;    //the actual timers
    reg signed m;    //feedback level multiplier
    reg  ch;
    l<=(potlim/32);//frequency cutoff
    m<=(potlim/256);//resonance level
    ch<=ch+1;        //8channels, clock through them all
    in = ((audioout+(audioout*m)/32)-((yaudio*m)/8))*4; //do feedback and input
    wa = ((wc * a2) + (wb * a1) + (in /2))/64;        //do filtering
    ac = (wa * b0) + (wb * b1) + (wc * b2);        //do more filtering
    
    if (co++>=l) begin co=0; wc <= wb; wb <= wa; end  //rotate data for filter
    if (co++>=l) begin co=0; wc <= wb; wb <= wa; end  //faster = higher cutoff
    if (co++>=l) begin co=0; wc <= wb; wb <= wa; end  //at different speeds
    if (co++>=l) begin co=0; wc <= wb; wb <= wa; end
    if (co++>=l) begin co=0; wc <= wb; wb <= wa; end
    if (co++>=l) begin co=0; wc <= wb; wb <= wa; end
    if (co++>=l) begin co=0; wc <= wb; wb <= wa; end
    if (co++>=l) begin co=0; wc <= wb; wb <= wa; end
 
    end
    assign     yaudio = ac/256/2;    //do output levelchange
    assign     yaudio = ac/256/2;    //to be able to use all bits
    assign     yaudio = ac/256/2;    //input also does this
    assign     yaudio = ac/256/2;    //and center too
    assign     yaudio = ac/256/2;
    assign     yaudio = ac/256/2;
    assign     yaudio = ac/256/2;
    assign     yaudio = ac/256/2;