Topic: Communication Systems
If $f(t)$ is 1 MHz sinusoid with 1 $V_{p-p}$ and sampling frequency $f_{s}$ is 25 kHz, the output of an A/D followed by D/A converter will be
- A. 0 V
- B. DC value anywhere between -1 V and +1 V
- C. DC value anywhere between -0.5 V and +0.5 V
- D. 1 $V_{p-p}$ 1 MHz sinusoid
Answer: C. DC value anywhere between -0.5 V and +0.5 V
Explanation: The signal frequency is $1\text{ MHz}$ ($1000\text{ kHz}$) and the sampling frequency is $25\text{ kHz}$. Since $1000\text{ kHz}$ is an exact integer multiple of $25\text{ kHz}$ ($1000/25 = 40$), the samples are taken at the exact same phase of the sine wave in every cycle. This causes the sampled signal to be a constant DC value. Since the input is a $1\text{ V}_{p-p}$ sinusoid (ranging from -0.5 V to +0.5 V), the resulting DC value can be anywhere in the range of -0.5 V to +0.5 V.