Question

3. Create an m-file myidftloop.m that takes as input a column vector Fr of DFT co- efficients and produces as output the corresponding column vector fk of samples, according to the formula

   1 N0−1 2πrk
   fk= ?FrejN0 , k=0,1,...,N0−1.

   Again, your code should automatically determine N0 based on the length of the input vector Fr. To compute the inverse DFT, you should use a nested loop. Hand in your m-file and make sure it is clearly documented.

4. Validate your m-file by running the following code (include a copy of the output at the command line):

T = 0.1e-3;
N0 = 128;
T0 = N0*T;
ft = inline(’cos(2*pi*1100*t)’);
fk = T*ft([0:1:N0-1]’*T);

Fr = mydftloop(fk);
fkrecon = myidftloop(Fr);
maxError = max(abs(fk-fkrecon))

% this should be very small

Answer 1

function Fr = mydftloop(fk);
N=length(fk)
for k=0:1:N-1
    sum=0
    for n=0:1:N-1
      sum=sum+(fk(n+1)*exp(-j*2*pi*(k)*n/N));
    Fr(k+1)=sum;
end
end
end

________________________________________________________

function fkr = myidftloop(Fr);
N=length(Fr)
for n=0:1:N-1
    sum=0
    for k=0:1:N-1
    sum=sum+(Fr(k+1)*exp(j*2*pi*k*n/N));
    fkr(n+1)=sum;
end
end
fkr=fkr/N
end

_________________________________________________________

Command window:

maxError =    3.8135e-18

Hint:

The last line of the calling script should be

maxError = max(abs(fk'-fkrecon))