# BFSK Modulation Output

I'm having trouble understanding outputs of a BFSK modulator.

$$S_1(t) = cos(πt/T)$$ $$S_2(t) = cos(2πt/T)$$

If the input 0 or 1, how can I calculate the output?

Edit:

There is a formula to calculate the output:

$$Zi(t) = ∫ r(t)S_i(t)dt$$

If the input is $S_2$ what will be the outputs and decision? I couldn't find any examples for these formula. Any help is greatly appreciated.

BFSK uses a pair of discrete frequencies to transmit binary (0s and 1s) information. $s_1(t)$ and $s_2(t)$ are the discrete frequency signals here. $s_1(t)$ has a frequency of $1/2T$ and $s_2(t)$ has a frequency of $1/T$. But your question does not say which signal is sent for input $0$.

So if $s_1(t)$ is sent for input $0$ and $s_2(t)$ is sent for input $1$, then the output is given by

$$y(t) = \overline{x(t)}\ s_1(t)+x(t)\ s_2(t)$$

where, $x(t) \in \{0,1\}$ is the input and $\overline{x(t)}=1-x(t)$.

EDIT:
In a FSK demodulator, the received signal, $r(t)$ is correlated with signal corresponding to each symbol, $S_i(t)$ to get $Z_i(t)$.

$$Z_i(t) = \int r(t)\ s_i(t)\ dt\tag1$$ Then the demodulator makes a decision based on the value of $Z_i(t)$. The decision is made in favor of i$^{th}$ symbol producing maximum correlation product ($Z_i(t)$)

So in BFSK, the received signal $r(t)$ is correlated with both $s_1(t)$ and $s_2(t)$. So if 1 be the value of modulating signal, then $s_2(t)$ is the received signal and its correlation product with s1(t) and s2(t) are calculated using equation (1). Correlating $s_2(t)$ with itself will produce the maximum value and hence the demodulator makes a decision in favor of $s_2(t)$.

• Thanks nidhin. I edited the question, could you please take a look. – Jenny94 Jul 6 '14 at 13:53
• I calculated z1(t)=0 and, z2(t)=T/2 when s2(t) is the received signal. So what does this mean? – Jenny94 Jul 6 '14 at 16:38
• @Jenny94 It means that the received signal is more 'related' to s2(t) than s1(t). – nidhin Jul 6 '14 at 16:58