Periodic Signals Concept of periodic signal The same signal pattern repeats over time Otherwise, a signal is aperiodic ine Wave: represented by three parameters riod=T=l/ s(0)=4sin(2f+p) (a) Sine way Peak Amplitude(a) maximum strength of signal measured in volts Frequency (f) Rate of change of signal Hertz(Hz) or cycles per second Period =time for one repetition(t) T=1/f Phase(q Relative position in time within a single period of a signal Figure(a) displays the value of a signal at a period =T=1/ given point in space as a function of time (b)Square wave
11 Periodic Signals Concept of periodic signal • The same signal pattern repeats over time. • Otherwise, a signal is aperiodic . Sine Wave: represented by three parameters, s(t)=Asin(2 ft+) • Peak Amplitude (A) — maximum strength of signal — measured in volts • Frequency (f) — Rate of change of signal — Hertz (Hz) or cycles per second — Period = time for one repetition (T) — T = 1/f • Phase () — Relative position in time within a single period of a signal Figure (a) displays the value of a signal at a given point in space as a function of time
Varying Sine Waves s(t)=Asin(2ft+Φ) a)A=1,f=1,0=0 b)A=05J=1,中=0 s(n s() 12
12 Varying Sine Waves s(t) = A sin(2ft +)
Signals: Frequency Domain In practice, an electromagnetic signal will be made up of many fre equencies a frequency means a pure sine wave Asin (2rft+o It can be shown(by Fourier analysis)that any signal is made up of components at various frequencies, in which each component is a sinusoid By adding together enough sinusoidal signals, each with the appropriate amplitude, frequency, and phase, any electromagnetic signal can be constructed - Any electromagnetic signal can be shown to consist of a collection of periodic analog signals(sine waves )at different amplitudes, frequencies, and phases Frequency domain function of a signal: S(f) u pecifies the peak amplitude of the constituent frequencies of the S e gnal 13
13 Signals: Frequency Domain • In practice, an electromagnetic signal will be made up of many frequencies. —A frequency means a pure sine wave Asin(2 ft+) • It can be shown (by Fourier analysis) that any signal is made up of components at various frequencies, in which each component is a sinusoid. —By adding together enough sinusoidal signals, each with the appropriate amplitude, frequency, and phase, any electromagnetic signal can be constructed. —Any electromagnetic signal can be shown to consist of a collection of periodic analog signals (sine waves) at different amplitudes, frequencies, and phases. • Frequency domain function of a signal: S(f) —Specifies the peak amplitude of the constituent frequencies of the signal
Addition of Frequency Components 0. 07 0.5T 1.0T 2.0T T=1) 0.0T 0.5T 1.07 1.5T 20T This signal has only two 1+ frequency components (1)frequency f (2) frequency 3f 0.5 0.0T 1.5T 20T (e)(4/x)lsin(2t+(13)sin(2t(30
14 Addition of Frequency Components (T=1/f) This signal has only two frequency components: (1) frequency f (2) frequency 3f
Frequency 4/π Domain ←(4/π)sin2ft Representations 4/3 0.4 (4/3I sin2(3ft This signal is the same as 0.0 signal( c)in the previous If 2 J (a)s(n)=(4) sin(mfn)+(1/3) sin(2 i3/)nl slide .2X 0.8X 0,6X This signal has infinite 0.4X number of frequency components: from 0 to infinity 0.0X 0.4 1/X b)s(n)=1-X2≤ts
15 Frequency Domain Representations This signal has infinite number of frequency components: from 0 to infinity 4/π 4/3π (4/π)sin2πft (4/3π)sin2π(3f)t This signal is the same as signal (c) in the previous slide