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| What are the two (2) main types of Pulse Modulation? |
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Definition
1) Analog Pulse Modulation
2) Digital Pulse Modulation |
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| The periodic pulse train is used as a carrier wave. |
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| Characteristic of Analog Pulse Modulation |
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| Some feature of each pulse (amplitude, duration or position) is varied in a continuous manner in accordance /w the corresponding sample value of the message signal. |
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| Characteristic of Analog Pulse Modulation |
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| Information transmitted in analog form, but transmission takes place at discrete times. |
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| Characteristic of Analog Pulse Modulation |
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| Message information is coded & transmitted in a pulse form that is discrete in both time & amplitude. |
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| Characteristic of Digital Pulse Modulation |
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| Information transmitted in digital form as a sequence of coded pulses. |
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| Characteristic of Digital Pulse Modulation |
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| It has no continuous wave (CW) counter-part. |
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| Characteristic of Digital Pulse Modulation |
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| The Sampling Process is basic to... |
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| It's basic to all pulse modulation systems (be it analog or digital), digital signal processing, & digital communication systems |
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| Through the use of the Sampling Process, an analog signal is... |
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| It is transformed/converted to a corresponding sequence of samples that are usually spaced uniformly in time. |
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| The Essence of the Sampling Process |
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| Let g(t) be an arbitrary signal of finite energy, which is specified for all time. |
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| Suppose we sample g(t) instantaneously at uniform rate (every Ts seconds). |
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| This yields an infinite sequence of samples which are spaced Ts apart {g(nTs)} where n=1, 2, 3,... |
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| It's referred to as the Sampling Period. |
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Let gδ(t) denote the signal obtained by individually weighting the elements of a periodic sequence of delta functions spaced Ts apart by the sequence numbers {g(nTs)}
gδ(t) = Σn g(nTs) δ(t-nTs) |
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| g(nTs) → "mass" assigned to the delta function δ(t-nTs) |
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g(nTs) → "mass" assigned to the delta function δ(t-nTs)
- Rectangular pulses of duration Δt & amplitude g(nTs)/(Δt)
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g(nTs) → "mass" assigned to the delta function δ(t-nTs)
- The smaller Δt gets, the better this apprximation becomes
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| The process of uniformly sampling continuous-time signal of finite energy results in a periodic spectrum /w a period equal to the sampling rate |
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How is a band-limited signal of finite energy is completely described?
The Sampling Theorem |
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By specifying the values of the signal at instants of time separated by 1/(2W) seconds
[1/(2W) is referred to as the Nyquist Interval] |
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| A band-limited signal of finite energy has no frequency components higher than W (Hertz) |
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| A band-limited signal of finite energy may be completely recovered from a knowledge of its samples taken at a rate of 2W samples per second. |
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| A band-limited signal of finite energy has no frequency components higher than W (Hertz). |
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| The sampling rate of 2W samples per second is called...
Sampling Theorem
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| The derivation of the sampling theorem is based on the assumption that the message signal is...
Sampling Theorem
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| Some degree of undersampling occurs. |
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Definition
Sampling Theorem
"Due to the practice not being practical..." |
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| Some aliasing is produced by the sampling process. |
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Definition
Sampling Theorem
"Due to the practice not being practical..." |
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This refers to the phenomenon of a high-frequency component in the spectrum of the signal taking on the identity of a lower-frequency.
Sampling Theorem |
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Definition
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"To combat the effects of aliasing..."
Sampling Theorem |
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| A low-pass anti-aliasing filter is used prior to sampling. |
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At what rate is the Filtered signal sampled at?
Sampling Theorem |
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| A rate slightly higher than the Nyquist Rate. |
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What are the amplitude of regularly spaced pulses are varied in proportion to?
Pulse Amplitude Modulation (PAM) |
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| The corresponding samples of a continuous message signal. |
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What are some qualities of Pulse Amplitude Modulation (PAM)?
Pulse Amplitude Modulation (PAM) |
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- Looks like natural sampling.
- The top of each pulse is flat.
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What are qualities of "Natural Sampling"?
Pulse Amplitude Modulation (PAM)
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- Natural sampling: samples are "pulse like".
- The tops vary in accordance to the message.
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| The basic ingredient in the application of digital communications is... |
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| This is is represented by the use of coded pulses for the transmission of analog information-bearing signals |
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- Instantaneous sampling of m(t)
- Every Ts seconds & according to sampling theorem
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Definition
Pulse Amplitude Modulation
"Two operations involved"
Sample & Hold |
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| Lengthening the duration of each sample to some constant value T (pulse width) |
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Definition
Pulse Amplitude Modulation
"Two operations involved"
Sample & Hold |
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- Imposes stringent requirements on the magnitude & phase responses of the channel.
- Noise performance of a PAM system can not be better than that of baseband transmission.
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Definition
Pulse Amplitude Modulation
Problems with PAM |
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| It's only good as a step within some more sophisticated form of pulse |
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Definition
Pulse Amplitude Modulation
What's it good for? |
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| The Sampling Process is usually described in... |
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Definition
| It's usually described in the time domain. |
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| The Sampling Process is an operation that is basic to... |
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Definition
| It's basic to all pulse modulation systems (be it analog or digital), digital signal processing, & digital communication systems |
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| fs = 1/Ts is referred to as... |
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| It's referred to as the Sampling Rate. |
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| gδ(t) is referred to as... |
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| It's referred to as the Ideal Sampled Signal. |
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| The term δ(t-nTs) represents a... |
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| It represents a delta function positioned at time t=nTs |
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How may we combat the effect of Aliasing?
Sampling Theorem |
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Definition
- A low pass anti-aliasing filter is used
(prior to sampling)
- (Next) The filtered signal is then sampled at a rate slightly higher than the "Nyquist Rate".
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What type of signal has the amplitude of regularly spaced pulses varied in proportion to the corresponding samples?
Pulse Amplitude Modulation (PAM) |
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Definition
| A conitinuous message signal |
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What's the difference between "Natural Sampling" & "Pulse Amplitude Modulation"?
Pulse Amplitude Modulation (PAM) |
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Definition
Natural Sampling
- Their tops are not flat but, vary with the message
Pulse Amplitude Modulation (PAM)
- The top of each pulse is flat
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What are the two (2) operations involved with Pulse Amplitude Modulation (PAM)?
Pulse Amplitude Modulation (PAM)
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Definition
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What type of sampling of m(t) occurs every Ts seconds?
Pulse Amplitude Modulation (PAM) |
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Definition
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This is the best analog pulse modulation technique in terms of noise performance
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Definition
| Pulse Position Modulation (PPM) |
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What are some of the problems of Pulse Amplitude Modulation (PAM)?
Pulse Amplitude Modulation (PAM) |
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Definition
- Imposes stringent requirements on the magnitude & phase responses of the channel
- Noise Peformance of a PAM system can not be better than that of baseband transmission
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What type of modulation is only good as a step within some more sophisticated form of pulse modulation.
Pulse Amplitude Modulation (PAM) |
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Definition
| Pulse Amplitude Modulation (PAM) |
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Name the different types of Analog Pulse Modulation.
Pulse Amplitude Modulation (PAM) |
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Definition
- Pulse Duration Modulation (PDM)
(Also known as Pulse Width Modulation)
- Pulse Position Modulation (PPM)
- Pulse Amplitude Modulation (PAM)
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The system's noise performance can be improved by representing the sample values of message signal in terms of
Other Forms of Analog Pulse Modulation (PAM) |
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Definition
"...variation in a property other than the pulse amplitude."
PWM or PDM
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PPM |
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How may noise affect a Pulse Position Modulated (PPM) signal?
Other Forms of Analog Pulse Modulation (PAM) |
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Definition
| By falsifying the time at which the modulated pulses are judged to occur. |
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How may immunity to noise be established?
Other Forms of Analog Pulse Modulation (PAM)
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Definition
| By making the pulse build up so rapidly that the time interval during which noise can exert any pertubation is very short. |
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What are some qualities of Pulse Position Modulation (PPM)?
Other Forms of Analog Pulse Modulation (PAM) |
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Definition
- They have thresholds of its own
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What do Pulse Position Modulation (PPM) & Frequency Modulation (FM) have in common?
Other Forms of Analog Pulse Modulation (PAM) |
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Definition
| They exhibit similar noise performances. |
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Name some of the qualities Pulse Position Modulation (PPM) & Frequency Modulation (FM) have in common?
Other Forms of Analog Pulse Modulation (PAM) |
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Definition
- They have a comparable noise "trade-off" of transmission bandwidth for improved noise performance
- As good as it gets for Analog Modulation
(Continuous Wave Modulation & Analog Pulse Modulation) |
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Why do we go from Analog to Digital?
Why Digitize Analog Sources? |
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- Digital systems are less sensitive to noise
- It is easier to integrate many functionalities into the same digital system
- Digital circuitry is easier to repeat
- Efficient utilization of transmission media
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