vcd fft(const vcd& a, bool invert=false)
{
int n = a.size();
vcd A(a.size());
for(int i=0, j=0; i<a.size(); ++i)
{
A[j] = a[i];
int bit = n>>1;
for(; j>=bit && bit>1; bit>>=1)
j -= bit;
j += bit;
}
for(int s=2; s<=n; s<<=1)
{
double ang = 2 * pi / s * (invert ? -1 : 1);
cd ws(cos(ang), sin(ang));
for(int j=0; j<n; j+=s)
{
cd w=1;
for(int k=0; k<s/2; k++)
{
cd u = A[j+k];
cd t = A[j+s/2+k];
A[j+k] = u + w * t;
A[j+s/2+k] = u - w * t;
w *= ws;
}
}
}
if(invert)
foreach(i,A)
A[i] /= n;
return A;
}
void fft_inv(vcd& a) {
fft(a);
for (int i = 0; i < N; ++i) {
a[i] /= N;
}
//now we have the identity matrix from the bottom to top
reverse(a.begin() + 1, a.end());
}
void fft(vcd &a, bool invert)
{
int n = a.size();
if (n == 1)
return;
vcd a0, a1;
a0.resize(n / 2); a1.resize(n / 2);
for (int i = 0, j = 0; i < n; i += 2, ++j)
{
a0[j] = a[i];
a1[j] = a[i + 1];
}
fft(a0, invert);
fft(a1, invert);
double ang = 2 * 3.14159265359 / n * (invert ? -1 : 1);
complex<double> w(1), wn(cos(ang), sin(ang));
for (int i = 0; i < n / 2; ++i)
{
a[i] = a0[i] + (w * a1[i]);
a[i + n / 2] = a0[i] - (w * a1[i]);
w = w * wn;
}
if (invert)
{
for (int i = 0; i < n; ++i)
a[i] /= 2;
}
}
double rms(vcd v)
{
int num = v.size();
double temp = 0.0;
vd temp_v(num);
for (int z=0; z<num; z++) {temp_v[z]=pow(abs(v[z]),2);} // t1=abs(v)^2
temp = accumulate(&temp_v[0],&temp_v[num-1],temp_v[num-1])/(1.0*num); // t2=mean(t1)
temp = sqrt(temp); // rms=sqrt(t2)
return temp;
}
vcd fft(const vcd & v, bool inverse = false) {
static const double PI = acos(-1.0);
int n = v.size(), k = 0, high1 = -1;
while ((1 << k) < n) k++;
std::vector<int> rev(n);
rev[0] = 0;
for (int i = 1; i < n; i++) {
if ((i & (i - 1)) == 0) high1++;
rev[i] = rev[i ^ (1 << high1)];
rev[i] |= (1 << (k - high1 - 1));
}
vcd roots(n), res(n);
for (int i = 0; i < n; i++) {
double alpha = 2 * PI * i / n;
roots[i] = cd(cos(alpha), sin(alpha));
}
for (int i = 0; i < n; i++) res[i] = v[rev[i]];
for (int len = 1; len < n; len <<= 1) {
vcd tmp(n);
int rstep = roots.size() / (len * 2);
for (int pdest = 0; pdest < n;) {
int p1 = pdest;
for (int i = 0; i < len; i++) {
cd val = roots[i * rstep] * res[p1 + len];
tmp[pdest] = res[p1] + val;
tmp[pdest + len] = res[p1] - val;
pdest++, p1++;
}
pdest += len;
}
res.swap(tmp);
}
if (inverse) {
for (int i = 0; i < (int)res.size(); i++) res[i] /= v.size();
std::reverse(res.begin() + 1, res.end());
}
return res;
}
void init() {
int hb = -1;
rev.assign(N, 0);
_root.assign(N, 0);
for (int i = 1; i < N; ++i) {
if ((i & (i - 1)) == 0) {
++hb;
}
rev[i] = rev[i ^ (1 << hb)];
rev[i] |= (1 << (LOG - hb - 1));
}
for (int i = 0; i < N; ++i) {
ld angle = 2.0 * PI * i / (1.0 * N);
_root[i] = cd(cosl(angle), sinl(angle));
}
}
void FFT(vcd & IN,vcd & OUT,int n,bool perform_inv){
bit_rev(IN,OUT,n);
for(int s = 1,lg = len(n) - 1;s <= lg;s++){
int m = (1 << s);
cd wm = cd(cos(2.0*PI/m),sin(2.0*PI/m));
for(int k = 0;k < n;k += m){
cd w = cd(1.0,0.0);
for(int j = 0;j < m/2;j++){
cd t = w*OUT[k + j + m/2];
cd u = OUT[k + j];
OUT[k + j] = u + t;
OUT[k + j + m/2] = u - t;
if(perform_inv) w /= wm;
else w *= wm;
}
}
}
if(perform_inv) for(int i = 0;i < OUT.size();i++) OUT[i] /= n;
}
void display(vi E,vcd st,vi du,vi dc,vi sym,vcd s,vcd n,vcd r,vi sym_est,vi sym_err,vi destu,vi destc,vi berru,vi berrc)
{
cout << endl;
cout<<" Symbol Table: "; for(int n=0;n<st.size();n++){cout<< st[n]<<" ";} cout<<endl;
//cout<<" RMS: " << RMS <<endl;
//cout << endl;
//cout<<" Signal TX: "; for (int z=0;z<s.size();z++){cout<<s[z]<<" ";} cout<<endl;
//cout<<" Noise: "; for (int z=0;z<n.size();z++){cout<<n[z]<<" ";} cout<<endl;
//cout<<" Signal RX: "; for (int z=0;z<r.size();z++){cout<<r[z]<<" ";} cout<<endl;
cout << endl;
cout<<" Sym. Ind. TX: "; for(int z=0;z<sym.size();z++){cout<<sym[z]<<" ";} cout<<endl;
cout<<" Sym. Ind. Est.: "; for(int z=0;z<sym_est.size();z++){cout<<sym_est[z]<<" ";} cout<<endl;
cout<<" Sym. Error: "; for(int z=0;z<sym_err.size();z++){cout<<sym_err[z]<<" ";} cout<<endl;
cout << endl;
cout<<" Data (Coded): "; for(int z=0;z<dc.size();z++){cout<<dc[z];} cout<<endl;
cout<<" Data Est. (Coded): "; for(int z=0;z<destc.size();z++){cout<<destc[z];} cout<<endl;
cout<<" Bit Error (Coded): "; for(int z=0;z<berrc.size();z++){cout<<berrc[z];} cout<<endl;
cout << endl;
cout<<" Data (Uncoded): "; for(int z=0;z<du.size();z++){cout<<du[z];} cout<<endl;
cout<<"Data Est. (Uncoded): "; for(int z=0;z<destu.size();z++){cout<<destu[z];} cout<<endl;
cout<<"Bit Error (Uncoded): "; for(int z=0;z<berru.size();z++){cout<<berru[z];} cout<<endl;
cout << endl;
}