Pulse Amplitude Modulation and Demodulation

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Pulse Amplitude Modulation and Demodulation

📘 Overview & Theory of Pulse Amplitude Moduation (PAM)
🧮 Pulse Amplitude Demoduation
🧮 MATLAB Code for PAM
📚 Further Reading

🧮 Simulation results for comparison of PAM, PWM, PPM, DM, and PCM
🧮 Other Pulse Modulation Techniques (e.g., PWM, PPM, DM, and PCM)
🧮 MATLAB Code for Pulse Amplitude Modulation and Demodulation of an Analog Signal (2)
🧮 MATLAB Code for Pulse Amplitude Modulation and Demodulation of Digital data

Pulse Amplitude Modulation (PAM)

Sampling allow us to represent real world continuous signal, such as audio or video, in a format suitable for digital processing and storage. This sampled discrete-time signal is inherently digital. A digital signal is a discrete-time signal that is further quantized in amplitude.

Pulse Amplitude modulation (PAM) is the modulation technique in which amplitude of carrier pulses is made to vary in accordance with the input message signal, similar to Amplitude Modulation (AM). But here we use pulse generator as carrier signal. So, Pulse–amplitude modulation (PAM) is a form of signal modulation where the message information is encoded in the amplitude of a series of signal pulses.

Fig 1: Pulse Amplitude Modulation

The basic idea in PAM for communication over a Continuous Time (CT) channel is to transmit a sequence of Continuous Time pulses of some per-specified pulse shape, with the sequence of pulse amplitudes carrying the information.

Pulse Amplitude Demodulation

To demodulate a PAM signal, pass it through a reconstruction filter. As here, the amplitude of the pulse carrier is varied according to the amplitude of the message signal, we only need to pass this received pulse signal through a low-pass filter with a cut-off frequency the same as the message signal or slightly higher.

If you perform quantization at the transmitter side and assign some levels (amplitude levels), then demodulation is performed by detecting the amplitude level of the carrier at every single period. The number of possible pulse amplitudes in analog PAM is theoretically infinite. Digital PAM reduces the number of pulse amplitudes to some power of two. For example, in 4-level PAM there are (2^2 = 4) possible discrete pulse amplitudes; in 8-level PAM there are (2^3 = 8) possible discrete pulse amplitudes; and in 16-level PAM there are (2^4 = 16) possible discrete pulse amplitudes.

📘 Overview of BER and SNR 🧮 Online Simulator for BER calculation of m-ary QAM and m-ary PSK 🧮 MATLAB Code for BER calculation of M-ary QAM, M-ary PSK, QPSK, BPSK, ... 📚 Further Reading 📂 View Other Topics on M-ary QAM, M-ary PSK, QPSK ... 🧮 Online Simulator for Constellation Diagram of m-ary QAM 🧮 Online Simulator for Constellation Diagram of m-ary PSK 🧮 MATLAB Code for BER calculation of ASK, FSK, and PSK 🧮 MATLAB Code for BER calculation of Alamouti Scheme 🧮 Different approaches to calculate BER vs SNR What is Bit Error Rate (BER)? The abbreviation BER stands for Bit Error Rate, which indicates how many corrupted bits are received (after the demodulation process) compared to the total number of bits sent in a communication process. BER = (number of bits received in error) / (total number of tran...

Shannon Limit Explained: Negative SNR, Eb/No and Channel Capacity

Understanding Negative SNR and the Shannon Limit Understanding Negative SNR and the Shannon Limit An explanation of Signal-to-Noise Ratio (SNR), its behavior in decibels, and how Shannon's theorem defines the ultimate communication limit. Signal-to-Noise Ratio in Shannon’s Equation In Shannon's equation, the Signal-to-Noise Ratio (SNR) is defined as the signal power divided by the noise power: SNR = S / N Since both signal power and noise power are physical quantities, neither can be negative. Therefore, the SNR itself is always a positive number. However, engineers often express SNR in decibels: SNR(dB) When SNR = 1, the logarithmic value becomes: SNR(dB) = 0 When the noise power exceeds the signal power (SNR < 1), the decibel representation becomes negative. Behavior of Shannon's Capacity Equation Shannon’s channel capacity formula is: C = B log₂(1 + SNR) For SNR = 0: log₂(1 + SNR) = 0 When SNR becomes smaller (in...

Amplitude, Frequency, and Phase Modulation Techniques (AM, FM, and PM)

📘 Overview 🧮 Amplitude Modulation (AM) 🧮 Online Amplitude Modulation Simulator 🧮 MATLAB Code for AM 🧮 Q & A and Summary 📚 Further Reading Amplitude Modulation (AM): The carrier signal's amplitude varies linearly with the amplitude of the message signal. An AM wave may thus be described, in the most general form, as a function of time as follows: When performing amplitude modulation (AM) with a carrier frequency of 100 Hz and a message frequency of 10 Hz, the resulting peak frequencies are as follows: 90 Hz (100 - 10 Hz), 100 Hz, and 110 Hz (100 + 10 Hz). Figure: Frequency Spectrums of AM Signal (Lower Sideband, Carrier, and Upper Sideband) A low-frequency message signal is modulated with a high-frequency carrier wave using a local oscillator to make communication possible. DSB, SSB, and VSB are common amplitude modulation techniques. We find a lot of bandwidth loss in DSB. The bandwidth of S...

Analog vs Digital Modulation Techniques | Advantages of Digital ...

Modulation Techniques Analog vs Digital Modulation In our previous discussion, we explored the necessity of modulation. In this article, we focus on the fundamental differences between analog and digital modulation. The primary distinction is that digital modulation uses a discrete digital signal to modify the carrier, whereas analog modulation uses a continuous analog signal. Advantages of Digital Modulation over Analog Modulation Bandwidth Efficiency: Digital techniques (like QAM) can transmit more data within a limited frequency range. Noise Resistance: Digital signals have superior resistance to noise because they can be perfectly regenerated. Multiplexing: It is much easier to multiplex various data types (audio, video, text) into a single digital stream. Higher SNR: Better noise immunity leads to a higher Signal-to-Noise Ratio (SNR). Increased Throughput: Modern digital techniques provide significantly higher data ...

Comparing Baseband and Passband Implementations of m-ary QAM

Let's assume your original digital message bitstream is: 0, 0, 1, 0, 0, 0, 1, 0, 1, 1 In 4-QAM, we group them into pairs: (00), (10), (00), (10), (11). Your baseband symbols are: Symbol 1 (Bits 00): -1.00 - j1.00 Symbol 2 (Bits 10): 1.00 - j1.00 Symbol 3 (Bits 00): -1.00 - j1.00 Symbol 4 (Bits 10): 1.00 - j1.00 Symbol 5 (Bits 11): 1.00 + j1.00 To transmit these symbols over a wireless medium, we modulate this baseband signal onto a high-frequency carrier (e.g., 50 Hz). This process creates the passband signal , where the information is stored in the phase and amplitude of the sine wave. Fig 1: 4-QAM Baseband I and Q Components Fig 2: 4-QAM Passband Modulated Signal In this example, the symbol rate is 5 symbols per second. Detailed Explanation 4-QAM Constellation Mapping In standard 4-QAM mapping, bits are converted to complex points on a grid: Bits...

Comparing Baseband and Passband Implementations of ASK, FSK, and PSK

📘 Overview 🧮 Baseband and Passband Implementations of ASK, FSK, and PSK 🧮 Difference betwen baseband and passband 📚 Further Reading 📂 Other Topics on Baseband and Passband ... 🧮 Baseband modulation techniques 🧮 Passband modulation techniques Baseband modulation techniques are methods used to encode information signals onto a baseband signal (a signal with frequencies close to zero). Passband techniques shift these signals to higher carrier frequencies for transmission. Here are the common implementations: Amplitude Shift Keying (ASK) [↗] : In ASK, the amplitude of the signal is varied to represent different symbols. Binary ASK (BASK) is a common implementation where two different amplitudes represent binary values (0 and 1). ASK is simple but susceptible to noise. ASK Baseband (Digital Bits) ASK Passband (Modulated Carrier) Fig 1: ASK Passband Modulation (...

Online Simulator for ASK, FSK, and PSK

Try our new Digital Signal Processing Simulator! Start Simulator for binary ASK Modulation Message Bits (e.g. 1,0,1,0) Carrier Frequency (Hz) Sampling Frequency (Hz) Run Simulation Simulator for binary FSK Modulation Input Bits (e.g. 1,0,1,0) Freq for '1' (Hz) Freq for '0' (Hz) Sampling Rate (Hz) Visualize FSK Signal Simulator for BPSK Modulation ...

Theoretical vs. simulated BER vs. SNR for ASK, FSK, and PSK (MATLAB Code + Simulator)

📘 Overview 🧮 Simulator for calculating BER 🧮 MATLAB Codes for calculating theoretical BER 🧮 MATLAB Codes for calculating simulated BER 📚 Further Reading BER vs. SNR denotes how many bits in error are received for a given signal-to-noise ratio, typically measured in dB. Common noise types in wireless systems: 1. Additive White Gaussian Noise (AWGN) 2. Rayleigh Fading AWGN adds random noise; Rayleigh fading attenuates the signal variably. A good SNR helps reduce these effects. Simulator for calculating BER vs SNR for binary ASK, FSK, and PSK Calculate BER for Binary ASK Modulation Enter SNR (dB): Calculate BER Calculate BER for Binary FSK Modulation Enter SNR (dB): Calculate BER Calculate BER for Binary PSK Modulation Enter SNR (dB): Calculate BER BER vs. SNR Curves MATLAB Code for Theoretical BER % The code is written by SalimWireless.Com clc; clear; close all; % SNR va...

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