fft.cpp

// Copyright (c) 2005, Rodrigo Braz Monteiro
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/// @file fft.cpp
/// @brief Fast Fourier-transform implementation
/// @ingroup utility
///
/// Most of this code was taken from http://www.codeproject.com/audio/waveInFFT.asp
/// And rewriten by Rodrigo Braz Monteiro

#include "fft.h"

#ifndef WITH_FFTW3
#include <libaegisub/exception.h>

#include <cmath>

void FFT::DoTransform (size_t n_samples,float *input,float *output_r,float *output_i,bool inverse) {
	if (!IsPowerOfTwo(n_samples))
		throw agi::InternalError("FFT requires power of two input.");

	// Inverse transform
	float angle_num = 2.0f * 3.1415926535897932384626433832795f;
	if (inverse) angle_num = -angle_num;

	// Variables
	unsigned int i, j, k, n;
	float tr, ti;

	// Calculate needed bits
	unsigned int NumBits;
	NumBits = NumberOfBitsNeeded(n_samples);

	// Copy samples to output buffers
	for (i=0;i<n_samples;i++) {
		j = ReverseBits (i,NumBits);
		output_r[j] = input[i];
		output_i[j] = 0.0f;
	}

	unsigned int BlockEnd = 1;
	unsigned int BlockSize;
	for (BlockSize = 2;BlockSize<=n_samples;BlockSize<<=1) {
		// Calculate variables for this iteration
		float delta_angle = angle_num / (float)BlockSize;
		float sm2 = sin (-2 * delta_angle);
		float sm1 = sin (-delta_angle);
		float cm2 = cos (-2 * delta_angle);
		float cm1 = cos (-delta_angle);
		float w = 2 * cm1;
		float ar0, ar1, ar2, ai0, ai1, ai2;

		// Apply for every sample
		for(i=0;i<n_samples;i+=BlockSize) {
			ar1 = cm1;
			ar2 = cm2;
			ai1 = sm1;
			ai2 = sm2;

			for (j=i,n=0;n<BlockEnd;j++,n++) {
				k = j + BlockEnd;

				ar0 = w*ar1 - ar2;
				ai0 = w*ai1 - ai2;
				ar2 = ar1;
				ai2 = ai1;
				ar1 = ar0;
				ai1 = ai0;

				tr = ar0*output_r[k] - ai0*output_i[k];
				ti = ar0*output_i[k] + ai0*output_r[k];

				output_r[k] = output_r[j] - tr;
				output_i[k] = output_i[j] - ti;

				output_r[j] += tr;
				output_i[j] += ti;
			}
		}

		// Set next block end to current size
		BlockEnd = BlockSize;
	}

	// Divide everything by number of samples if it's an inverse transform
	if (inverse) {
		float denom = 1.0f/(float)n_samples;
		for (i=0;i<n_samples;i++) {
			output_r[i] *= denom;
			output_i[i] *= denom;
		}
	}
}

void FFT::Transform(size_t n_samples,float *input,float *output_r,float *output_i) {
	DoTransform(n_samples,input,output_r,output_i,false);
}

void FFT::InverseTransform(size_t n_samples,float *input,float *output_r,float *output_i) {
	DoTransform(n_samples,input,output_r,output_i,true);
}

/// @brief Checks if number is a power of two
bool FFT::IsPowerOfTwo (unsigned int x) {
	if (x < 2) return false;
	if (x & (x-1)) return false;
    return true;
}

/// @brief Bits needed by the FFT
unsigned int FFT::NumberOfBitsNeeded (unsigned int n_samples) {
	int i;

	if (n_samples < 2) {
		return 0;
	}

	for (i=0; ;i++) {
		if(n_samples & (1 << i)) return i;
    }
}

/// @brief Get reversed bit position
unsigned int FFT::ReverseBits (unsigned int index, unsigned int bits) {
	unsigned int i, rev;

	for(i=rev=0;i<bits;i++) {
		rev = (rev << 1) | (index & 1);
		index >>= 1;
	}

	return rev;
}

/// @brief Get frequency at index
float FFT::FrequencyAtIndex (unsigned int baseFreq, unsigned int n_samples, unsigned int index) {
	if (index >= n_samples) return 0.0;
	else if (index <= n_samples/2) {
		return ((float)index / (float)n_samples * baseFreq);
	}
	else {
		return (-(float)(n_samples-index) / (float)n_samples * baseFreq);
	}
}
#endif