Download Problems-Data Communication-Lecture Notes and more Study notes Data Communication Systems and Computer Networks in PDF only on Docsity!
LECTURE
Problems 4. A Sine wave has a frequency of 6 Hz. What is its period? Solution
Problems 4. A Sine wave completes one cycle in 4 seconds. What is its frequency? Solution:
Another Way to look at Frequency
- 17 sec 6
f
T
Hz T
f 0. 25 4
o Measurement of the rate of change o The rate at which a sine wave moves from its lowest to its highest point is its frequency o A 40 Hz signal has half the frequency of a 80 Hz signal, therefore each cycle takes twice as long to complete one cycle I.e. to go from its lowest to its highest o Change in a short Time = High Frequency
Two Extremes Frequency
o What if a signal does not change at all? o What if it maintains a constant voltage level the entire time? In such cases , Frequency is going to be zero
o If a signal does not change, it will never complete any cycles, and frequency is no. of cycles in 1 second so Freq = 0 o No change at all
- Zero frequency o Instantaneous changes
- Infinite frequency Phase o Phase describes the position of the waveform relative to time zero o If we think of the wave as something that can be shifted backward or forward along the time axis o Phase describes the amount of that shift o It indicates the status of the first cycle o Phase is measured in Degrees or Radians o 360 degrees – 2 pi Radians o A phase shift of 360 degrees correspond to a shift of a complete period o A phase shift of 180 degree correspond to a shift of half a period o A phase shift of 90 degree correspond to a shift of quarter a period
docsity.com
Problem 4. A sine wave is offset of a cycle with respect to time zero. What is its phase? Solution
One Cycle = 360 Degrees
of a cycle = = 60 Degrees
Control of Signals
o Signal can be controlled by three attributes: Amplitude Frequency Phase
Control of Signals- Amplitude
Control of Signals- Frequency
docsity.com
o Figure compares the time domain (instantaneous amplitude w.r.t Time) and the Frequency domain (Max amplitude w.r.t Frequency) o Low Frequency signal in frequency domain corresponds to a signal with longer period in Time domain & vice versa. o A signal changing rapidly in Time domain corresponds to High frequency in Frequency domain
o Figure shows 3 signals with different frequencies and its time and frequency domain
presentations
Composite Signals
o Second type of Analog Signals, that is composed of multiple sine waves o So far we have been focused on simple periodic signals or sine waves o Many useful sine waves do not change in a single smooth curve b/w minimum and maximum amplitude. o They jump, slide , wobble and spikeAs long as as any irregularities are consistent, cycle after cycle, a signal is still Periodic o It can be shown that any periodic signal no matter how complex can be decomposed into a collection of sine waves, each having a measurable amplitude, frequency & phase o We need FOURIER ANALYSIS to decompose a composite signal into its components
docsity.com
o Figure shows a periodic signal decomposed into two sine waves o First sine wave (middle one) has a frequency of ‘6’ while the second sine wave has a frequency of ‘0’ o Adding these two signals point by point results in the top graph o Original signal looks like a sine wave that has its time axis shifted downward o This shift is because of DC Component or zero frequency component in the signal o If you look at the signal in time domain, a single point is there while in frequency domain , two component freq.'s are there Summary
Sine Waves and its Characteristics Control of Signals Time and Frequency Domain Composite Signals
Reading Sections
Section 4.4, 4.5 “Data Communications and Networking” 4th Edition by Behrouz A. Forouzan
docsity.com
