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Frequency shift keying demodulation


z = fskdemod(y,M,freq_sep,nsamp) noncoherently demodulates the complex envelope y of a signal using the frequency shift key method.


z = fskdemod(y,M,freq_sep,nsamp,Fs) specifies the sampling frequency in Hz.

z = fskdemod(y,M,freq_sep,nsamp,Fs,symorder) specifies how the function assigns binary words to corresponding integers.


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Pass an FSK signal through an AWGN channel and estimate the resulting bit error rate (BER). Compare the estimated BER to the theoretical value.

Set the simulation parameters.

M = 2;         % Modulation order
k = log2(M);   % Bits per symbol
EbNo = 5;      % Eb/No (dB)
Fs = 16;       % Sample rate (Hz)
nsamp = 8;     % Number of samples per symbol
freqsep = 10;  % Frequency separation (Hz)

Generate random data symbols.

data = randi([0 M-1],5000,1);

Apply FSK modulation.

txsig = fskmod(data,M,freqsep,nsamp,Fs);

Pass the signal through an AWGN channel

rxSig  = awgn(txsig,EbNo+10*log10(k)-10*log10(nsamp),...

Demodulate the received signal.

dataOut = fskdemod(rxSig,M,freqsep,nsamp,Fs);

Calculate the bit error rate.

[num,BER] = biterr(data,dataOut);

Determine the theoretical BER and compare it to the estimated BER. Your BER value might vary because the example uses random numbers.

BER_theory = berawgn(EbNo,'fsk',M,'noncoherent');
[BER BER_theory]
ans = 1×2

    0.0958    0.1029

Input Arguments

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Complex baseband representation of a FSK-modulated signal, specfied as vector or matrix of complex values. If y is a matrix with multiple rows and columns, fskdemod processes the columns independently.

Data Types: double | single
Complex Number Support: Yes

Modulation order, specified as an integer power of two.

Example: 2 | 4 | 16

Data Types: double

Symbol order, specified as 'bin' or 'gray'. This argument specifies how the function assigns binary vectors to corresponding integers.

  • If symorder is 'bin', the function uses a natural binary-coded ordering.

  • If symorder is 'gray', the function uses a Gray-coded ordering.

Data Types: char

Desired separation between frequencies, specified in Hz. By the Nyquist sampling theorem, freq_sep and M must satisfy (M-1)*freq_sep <= 1.

Data Types: double

Number of samples per output symbol, specified as a positive scalar greater than 1.

Data Types: double

Sample rate, specified as a positive scalar.

Data Types: double

Output Arguments

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Output signal, returned as a vector or matrix of positive integers. The elements of z have values in the range of [0, M – 1].

Example: randi([0 3],100,1)

Data Types: double


[1] Sklar, Bernard. Digital Communications: Fundamentals and Applications. Upper Saddle River, NJ: Prentice-Hall, 2001.

Introduced before R2006a