# ASK and FSK: digital modulations

In our previous posts, we have studied analog modulations such as AM and FM and we introduced PAM and PWM as an intermediate step to achieve digital modulations.

In this post, we are going to analyse the two principal digital modulation schemes: ASK and FSK. We will see how they are generated in the time domain and their spectrum. Ready? 😉

### ASK SIGNALS (TIME AND FREQUENCY DOMAIN)

In order to generate an ASK signal in the time domain, we need to use a NRZ digital signal as the modulation signal and a sinusoidal carrier with frequency fc: we will multiply these two signals, and this is what we know as an ASK On-Off key, one of the simplest ASK modulators which assigns an amplitude to the “zero” value bit equal to zero. Figure 1. ASK signals in time and frequency domain
In the image above the sampling frequency is fs=100000 samples/second. The ASK carrier is a cosine signal with frequency fm=fs/5. Also, we can observe in the image the point where the spectrum amplitude falls 3 dB. This frequency (20500 Hz, approximately) is subtracted from the central frequency and multiplied by 2, in order to obtain the bandwidth, which you can compute and you should get 1 kHz.
The bandwidth is proportional to the baud rate. Half of the bandwidth is placed around the carrier frequency. Therefore, if we assume a band-pass channel, we can choose the carrier frequency to make the modulated signal occupy all the available bandwidth. ### FSK SIGNALS (TIME AND FREQUENCY DOMAIN)

One way to implement an FSK signal is by using to ASK signals with different carrier frequencies: Figure 3. FSK signal generation with 2 ASK signals
Therefore, we can use the same ASK signal studied in the previous section and another one with different carrier frequency to generate the following FSK signal in the time and frequency domains: Figure 4. FSK signal in time and frequency domains
As we did with the ASK signal, we have measured the bandwidth for the FSK signal: we have drawn a red line which represents a centered value between the two carrier frequencies. If we measure each -3dB amplitude point at each side and take the distance (in Hz) we will obtain a total bandwidth of 4.2 kHz, which is bigger than the one we saw for the ASK case. We can also measure the bandwidth between nulls and see that it is 19.6 kHz, approximately (also greater than the one corresponding to the ASK signal).
In addition, we can establish the relation between the bandwidth and the baud rate: Figure 5. FSK baud-rate
For low frequencies, the FSK bandwidth is related to the baud rate. For higher frequencies the bandwidth and the baud rate are related by the carrier frequencies’ shift. If Afc is the distance between both carrier frequencies, from the centered point between them, the difference between both frequencies is 2xAfc; that’s why the FSK bandwidth is greater than the corresponding for ASK.
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