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/*N is signal size (number of samples), sampleRate in kHz (num samples per ms), frameLength in ms, shiftLength in ms*/
vector<vector<Ciphertext<DCRTPoly>>> real_discrete_fourier_transform(int N, int sampleRate, int frameLength, int shiftLength, CryptoContext<DCRTPoly> cc, LPPublicKey<DCRTPoly> publicKey, CryptoFractions encSignal, LPPrivateKey<DCRTPoly> sk) {
	int boundN, boundM;

	if (N % 2 == 0) {
		boundM = N / 2 - 1;
		boundN = N / 2;
	}
	else {
		boundM = (N - 1) / 2;

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CryptoFractions encrypt_audio(vector<float> signal, int startIndex, int sampleSize, const char *keysFilePath, const long precision) {
	
	vector<int64_t> intSignal;
	CryptoFractions encryptedSignal;
	int numerator;
	int endIndex = startIndex + sampleSize;
	
	for (int i = startIndex; i < endIndex; i += 1) {
		numerator = int(signal[i] * precision);
		encryptedSignal.numerators.push_back(numerator);

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Plaintext calculate_sine_array(int m, int N, int start, int stop, CryptoContext<DCRTPoly> cc) {
	vector<int64_t> *sines = new vector<int64_t>();
	for (int k = 0; k != N; k++) {
		if (k < start || k >= stop) {
			sines->push_back(0);
			continue;
		}
		int sinVal = int(sin(((2 * pi * k * m) / N)) * 100); //FOR MORE ACCURATE RESULTS, INCREASE MULTIPLE OF 10
		sines->push_back(sinVal);
	}

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Plaintext calculate_cosine_array(int n, int N, int start, int stop, CryptoContext<DCRTPoly> cc) {
	vector<int64_t> *cosines = new vector<int64_t>();
	for (int k = 0; k != N; k++) {
		if (k < start || k >= stop) {
			cosines->push_back(0);
			continue;
		}
		int cosVal = int(cos(((2 * pi * k * n) / N)) * 100); //FOR MORE ACCURATE RESULTS, INCREASE MULTIPLE OF 10
		cosines->push_back(cosVal);
	}

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struct CryptoFractions {
	Ciphertext<DCRTPoly> encryptedNumerators;
	Ciphertext<DCRTPoly> encryptedDenominators;
	vector<int64_t> numerators;
	vector<int64_t> denominators;
};

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/*N is signal size (number of samples), sampleRate in kHz (num samples per ms), frameLength in ms, shiftLength in ms*/
vector<vector<Ciphertext<DCRTPoly>>> real_discrete_fourier_transform(int N, int sampleRate, int frameLength, int shiftLength, CryptoContext<DCRTPoly> cc, LPPublicKey<DCRTPoly> publicKey, CryptoFractions encSignal, LPPrivateKey<DCRTPoly> sk) {
	int boundN, boundM;

	if (N % 2 == 0) {
		boundM = N / 2 - 1;
		boundN = N / 2;
	}
	else {
		boundM = (N - 1) / 2;