Question

A signal 𝑣(𝑡) band limited to 𝑓 Hz is sampled by a periodic pulse train 𝑆(𝑡) made up of a rectangular pulses of width seconds (centered at the origin) at the Nyquist rate (2𝑓 pulses per second). Show that the samples signal 𝑣 𝑡 is given by: 𝑣 𝑡 𝑣 𝑡 ∑ ( ) 𝑣 𝑡 𝑐𝑜𝑠𝑛𝑤 𝑡 𝑤 𝜋𝑓 Show that the signal 𝑣(𝑡) can be recovered by passing 𝑣𝑠(𝑡)through an ideal low pass filter of bandwidth 𝑓𝑚 and a gain of 4