Sinusoidal waveform Where: Vis the instantaneous amplitude of the sine wave V m is the peak amplitude of the sine wave  is the angular frequency (2  f)of the sine wave tis the time in second

Sinusoidal waveform (cont.)

Types of signal a: Static: DCb: 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 sampling  Most 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 f sampling > f signal  o.k. Ideally f sampling ≥ 2 f signal  If f sampling < f signal  aliasing  Some applications don’t accept f sampling = 2 f signal as in ECG signal  = 5 f signal

Reconstruction of Sampled signals  To reconstruct the original signal after sampling  pass the sampled waveform through a low-pass filter that blocks f s  Sampling is used to form  AM, PM,