Sinusoidal waveform

Where:V is the instantaneous amplitude of the sine waveVm is the peak amplitude of the sine wave is the angular frequency (2f)of the sine wavet is the time in second

        

                                                                                    

       

Sinusoidal waveform (cont.)

Types of signal

a: Static: DC b: Quasistatic c: Periodic: sine,square,.. ,v(t)=v(t+T)

d: Repetitive: quasiperiodic

e: Single event transient signal

f: Repetitive single event

Waveform symmetry

A: Square wave with DC component that causes asymmetry

B: Symmetrical square wave

C: Sawtooth waveform forms mirror image across zero basline

D: Quarter-wave symmetry

A B

C D

Signal samplingMost instrumentation transducers have analog output

At the interface between analog transducers and digital computers the signal must be digitized

So the signal is sampled at regular intervals

Each sample voltage is then converted into an equivalent digital value

The next sample cannot be taken until the conversion of the last sample to digital form is completed

Sampled signals

A: continuous waveform

B: Sampled version of continuous waveform

C: Reconstructed waveform

A

B

C

Sampled signals

A: Sine wave

B: Sampling of sine wave

C: Sampled sine wave

A

B

C

Effect of the sampling rate

1 Sample/sec

12 sample/sec

If fsampling > fsignal o.k. Ideally fsampling ≥ 2 fsignal

If fsampling < fsignal aliasing

Some applications don’t accept fsampling= 2 fsignal

as in ECG signal = 5 fsignal

Reconstruction of Sampled signals

To reconstruct the original signal after sampling pass the sampled waveform through a low-pass filter that blocks fs

Sampling is used to formAM, PM,