Signal Representations PDF

Signal Representations Intended Learning Outcome Sketch the frequency domain equivalent of a given time domain wave using Fourier Series  Signal Representations 1. Time-Domain representation: ❏ graph: time vs (voltage or power) ❏ oscilloscope displays signals in time-domain 2...

Signal Representations Intended Learning Outcome Sketch the frequency domain equivalent of a given time domain wave using Fourier Series  Signal Representations 1. Time-Domain representation: ❏ graph: time vs (voltage or power) ❏ oscilloscope displays signals in time-domain 2. Frequency Domain Representation: ❏ graph: frequency vs (voltage or power) ❏ spectrum analyzer displays signals in frequency-domain Virtual Oscilloscope | Academo.org - Free, interactive, education. Oscilloscope Quiz | Academo.org - Free, interactive, education.  Example Sketch the given in frequency domain Solution: amplitude = 2V frequency = 440Hz  Why transform to frequency domain?. For communication engineers, the primary interest is what portion of the frequency spectrum does the signal occupy and how strong is the signal (magnitude); Part of the benefit of a frequency domain representation is that certain signal attributes, like bandwidth is visualized. Bandwidth (BW) is that portion of the electromagnetic spectrum occupied by a signal. BW = f2 - f1  Important to Note Working Example: 1. phase offset (if present) is not part of the frequency plot,, 2. a sine or cosine with the same amplitude (positive or negative) and any phase offset have the same frequency plot.  Fourier Theory ❏ In the real world, not all information signals are sinusoidal. ❏ Information signals can take on an infinite number of shapes, including rectangular waves (i.e., digital pulses), triangular waves, sawtooth waves, and other nonsinusoidal forms. ❏ Any well-behaved periodic waveform can be represented as a series of sine and/or cosine waves at multiples of its fundamental frequency plus (sometimes) a dc offset. This is known as a Fourier series.  Example Find the Fourier series for the signal in Figure and sketch its frequency domain equivalent to the fifth harmonics Solution: The given is sawtooth positive going (slide number 13) V = 5; T (period) = 1 ms; fo= 1/T = 1kHz Some waveforms have no dc components