Effect of Noise in Amplitude Modulation (AM)  Understanding the effect of noise in amplitude modulation (AM) is one of the most important topics in Analog Communication Systems.  This article explains the complete derivation step by step, including: Transmitted AM signal Received signal equation Why noise is written in envelope-phase form Difference between r(t) and y(t) Envelope detector output Threshold effect Step 1: Transmitted AM Signal The transmitted amplitude modulated (AM) signal is s(t)=A c [1+k a m(t)]cos(2πf c t) where A c = Carrier amplitude m(t) = Message signal k a = Amplitude sensitivity f c = Carrier frequency Step 2: Noise is Added by the Channel Every communication channel introduces random noise. Let the channel noise be n(t) The received signal becomes r(t)=s(t)+n(t) This is the most fundamental equation in communication systems. Received Signal = Transmitted...

FSK Modulation Simulator Frequency Shift Keying (FSK) Modulation Carrier 1 Frequency (Hz): Carrier 2 Frequency (Hz): Sampling Rate (Hz): Bit Rate (bps): Execute FSK Demodulation Execute FSK Demodulation Simulation Mathematics Digital FSK Signal Equation: s(t) = A_c cos(2π f_i t) f_i = f_1 for bit '1', f_i...

Instructions for Frequency Shift Keying Modulation (FSK) Step 1: Click on 'Generate Message' button to generate input message signal Step 2: Then click on 'Generate Carrier' button to generate carrier signal Step 3: You can change the carrier signal frequencies from the input fields Step 4: Click on 'Simulate FSK' button to generate Frequency Shift Keying Signal Carrier Frequency 1 in Hz: Carrier Frequency 2 in Hz: ...

Modulation vs. Multiplexing: Key Differences in Telecommunications Modulation vs. Multiplexing: Understanding the Foundation of Modern Communication In the world of telecommunications, Modulation and Multiplexing are often used interchangeably by beginners, but they represent two entirely different layers of signal processing. While one focuses on the integrity and speed of a single signal , the other focuses on the efficiency of the medium . Feature Modulation Schemes Multiplexing Techniques Core Definition Mapping information bits onto a physical carrier wave. Combining multiple data streams into one shared medium. Primary Objective Optimizing data rate and no...

Spectral Efficiency Lab Determine if your channel bandwidth supports your chosen modulation scheme. Bit Rate ($R_b$) in kbps Modulation Scheme BPSK / ASK (Binary) QPSK / 4-QAM (M=4) 8-PSK (M=8) 16-QAM (M=16) 64-QAM (M=64) Use Nyquist Min. BW ($B = R_s$) Default: Null-to-Null BW ($B = 2R_s$) Current Efficiency (η): 0.5 b/s/Hz Required Bandwidth for this setup: 20.00 kHz Signal Processing Knowledge Check Which modulation technique is most susceptible to power-line noi...

Why BPSK is 3dB Better Than BFSK? In digital communications, we are always fighting noise. The goal is to send bits (0 and 1) using the least amount of energy possible. If you compare **Binary Phase Shift Keying (BPSK)** and **Binary Frequency Shift Keying (BFSK)**, BPSK is the clear winner. Here is the mathematical "why." 1. BPSK (Antipodal) BPSK uses a single carrier but flips the phase. The symbols are "opposites." $d_{BPSK} = 2\sqrt{E_b}$ Distance is the full diameter of the circle. 2. BFSK (Orthogonal) BFSK uses two different frequencies. These act like two perpendicular dimensions. ...

Rigorous MSK/GMSK Visualizer BPSK vs MSK vs GMSK Simulation Bits: Mode: BPSK MSK GMSK BT: Amp Saturation: Simulate Phase Trajectory (Degrees) RF Waveform Spectrum (dB) Technical Analysis: Baseband to Passband Pipeline This simulator treats MSK and GMSK as Continuous Phase Modulation (CPM) systems, where information is encoded in the accumulation of phase rather than absolute state jumps. 1. The Pulse Shaping (NRZ to Frequency) Digital bits are mapped to NRZ (+1/-1) . In MSK/GMSK, these are treated as Frequency Commands . In GMSK, these pulses are convolved with a Gaussian filter: h(t) = (1/&sqrt;2πσT) exp(-t 2 /2σ 2 T 2 ) 2. Phase Accumulation (The Integral) The phase φ(t) is the integral of the shaped frequency pulses. For Minimum Shift Keying, the modulation index is exactly 0.5, ensuring a 90° shift per bit. BPSK Phase jumps instantly between 0 ...

Theoretical BER for MSK The theoretical Bit Error Rate (BER) for Minimum Shift Keying (MSK) is identical to that of BPSK (Binary Phase Shift Keying) and QPSK (Quadrature Phase Shift Keying), provided that coherent detection is used. The Formula The probability of bit error (\(P_b\)) for MSK is given by: \[P_b = Q\left(\sqrt{\frac{2E_b}{N_0}}\right)\] Alternatively, expressed using the complementary error function (\(\text{erfc}\)): \[P_b = \frac{1}{2} \text{erfc}\left(\sqrt{\frac{E_b}{N_0}}\right)\] Where: \(E_b\) : Energy per bit. \(N_0\) : Noise power spectral density (one-sided). \(E_b/N_0\) : The signal-to-noise ratio per bit. \(Q(x)\) : The Q-function, which represents the tail probability of the standard normal distribution. ...