Question

Situations in daily life where friction is not necessary

Answer 1

Impulse Sampling

Impulse sampling can be performed by multiplying input signal x(t) with impulse train [Math Processing Error] of period 'T'. Here, the amplitude of impulse changes with respect to amplitude of input signal x(t). The output of sampler is given by[Math Processing Error] impulse train[Math Processing Error][Math Processing Error]To get the spectrum of sampled signal, consider Fourier transform of equation 1 on both sides[Math Processing Error]This is called ideal sampling or impulse sampling. You cannot use this practically because pulse width cannot be zero and the generation of impulse train is not possible practically.

Natural Sampling

Natural sampling is similar to impulse sampling, except the impulse train is replaced by pulse train of period T. i.e. you multiply input signal x(t) to pulse train [Math Processing Error] as shown belowThe output of sampler is[Math Processing Error][Math Processing Error][Math Processing Error]The exponential Fourier series representation of p(t) can be given as[Math Processing Error][Math Processing Error]Where [Math Processing Error][Math Processing Error]Substitute Fn value in equation 2[Math Processing Error][Math Processing Error]Substitute p(t) in equation 1[Math Processing Error][Math Processing Error][Math Processing Error]To get the spectrum of sampled signal, consider the Fourier transform on both sides.[Math Processing Error][Math Processing Error]According to frequency shifting property[Math Processing Error][Math Processing Error]

Flat Top Sampling

During transmission, noise is introduced at top of the transmission pulse which can be easily removed if the pulse is in the form of flat top. Here, the top of the samples are flat i.e. they have constant amplitude. Hence, it is called as flat top sampling or practical sampling. Flat top sampling makes use of sample and hold circuit.Theoretically, the sampled signal can be obtained by convolution of rectangular pulse p(t) with ideally sampled signal say yδ(t) as shown in the diagram:i.e. [Math Processing Error]To get the sampled spectrum, consider Fourier transform on both sides for equation 1[Math Processing Error]By the knowledge of convolution property,[Math Processing Error]Here [Math Processing Error]

Nyquist Rate

It is the minimum sampling rate at which signal can be converted into samples and can be recovered back without distortion.Nyquist rate fN = 2fm hzNyquist interval = [Math Processing Error] = [Math Processing Error] seconds.

Samplings of Band Pass Signals

In case of band pass signals, the spectrum of band pass signal X[ω] = 0 for the frequencies outside the range f1 ≤ f ≤ f2. The frequency f1 is always greater than zero. Plus, there is no aliasing effect when fs > 2f2. But it has two disadvantages:The sampling rate is large in proportion with f2. This has practical limitations.The sampled signal spectrum has spectral gaps.To overcome this, the band pass theorem states that the input signal x(t) can be converted into its samples and can be recovered back without distortion when sampling frequency fs < 2f2.Also,[Math Processing Error]Where m is the largest integer < [Math Processing Error]and B is the bandwidth of the signal. If f2=KB, then[Math Processing Error]For band pass signals of bandwidth 2fm and the minimum sampling rate fs= 2 B = 4fm,the spectrum of sampled signal is given by [Math Processing Error] Previous PageNext Page  Advertisements