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Design of CMOS Flip-Flops (SR, D, JK)

Design of CMOS Flip-Flops (SR, D, JK) A flip-flop or latch is a circuit with two stable states, used to store state information. It is the basic storage element in sequential logic and a fundamental building block in digital electronics systems, including computers and communication devices. Flip-flops and latches act as data storage elements for states, pulse counting, and synchronization of variably-timed input signals to a reference clock. Flip-flops can be transparent/opaque (latches) or clocked (synchronous, edge-triggered). Latches are level-sensitive, while flip-flops are edge-sensitive. In sequential logic, the output depends on current inputs and previous states. Fig.1 shows a sequential circuit combining a combinational block and a memory element. ...
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Q-function in BER vs SNR Calculation (with Simulation)

Q-function in BER vs. SNR Calculation In digital communications and signal processing, the Q-function plays a significant role in predicting system reliability. It allows engineers to quantify the probability that Gaussian noise will exceed a specific threshold, causing a bit error. What is the Q-function? The Q-function is a mathematical function representing the tail probability of the standard normal (Gaussian) distribution. It is the complementary cumulative distribution function (CCDF) of a standard Gaussian distribution. Q(x) = (1 / √(2Ï€)) ∫â‚“∞ e^(-t² / 2) dt Q-Function Interactive Simulator Move the slider to see how the "Tail Probability" (the area in red) changes. This area represents the Probability of Error (BER) . Threshold Distance ( x ) — (Simulates Increasing SNR) x = 1.0 Q(x) = 0.1587 ...
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Pulse Width Modulation (PWM)

Pulse-width modulation (PWM), or pulse-duration modulation (PDM), is a method of controlling the average power delivered by an electrical signal.   Fig: An example of PWM in an idealized inductor driven by a blue line voltage source modulated as a series of sawtooth pulses, resulting in a red line current in the inductor.    Generating a PWM Signal The simplest way to generate a PWM signal is the intersection method, which requires only a sawtooth or a triangle waveform (easily generated using a simple oscillator) and a comparator. When the value of the reference signal is more than the modulation waveform, the PWM signal (magenta) is in the high state; otherwise, it is in the low state.      Duty cycle A low duty cycle equates to low power because the power is off for most of the time; the word duty cycle reflects the ratio of "on" time to the regular interval or "period" of time. The duty cycle is measured in percent, with 100% representing full o...
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FFT Butterfly Method Explained (with Example of 4-point DFT)

  FFT Using Butterfly Method Given: x[n] = {0, 1, 2, 3} Step 1: Split into Even & Odd Even indices: x e = {0, 2} Odd indices: x o = {1, 3} Step 2: 2-point DFT For any {a, b}: DFT = {a + b, a - b} Even Part: E = {0+2, 0-2} = {2, -2} Odd Part: O = {1+3, 1-3} = {4, -2} Step 3: Combine Using Butterfly X[k] = E[k] + W k O[k] X[k + N/2] = E[k] - W k O[k] For N = 4: W 0 = 1 W 1 = -j Final Calculations X[0] = 2 + 4 = 6 X[2] = 2 - 4 = -2 X[1] = -2 + (-j)(-2) = -2 + 2j X[3] = -2 - (-j)(-2) = -2 - 2j Final Answer: X[k] = {6, -2 + 2j, -2, -2 - 2j} Try Interactive Online Simulations Interactive FFT Online Simulator (For understanding Fundamentals)  Interactive FFT Online Simulator (Analyze .CSV, .MP3, .MP4, etc. Further Reading Fourier Transform OFDM Return to Fourier Transform Main Page →
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BER vs SNR for M-ary QAM, M-ary PSK, QPSK, BPSK, ...(MATLAB Code + Simulator)

Bit Error Rate (BER) & SNR Guide Analyze communication system performance with our interactive simulators and MATLAB tools. 📘 Theory 🧮 Simulators 💻 MATLAB Code 📚 Resources BER Definition SNR Formula BER Calculator MATLAB Comparison 📂 Explore M-ary QAM, PSK, and QPSK Topics ▼ 🧮 Constellation Simulator: M-ary QAM 🧮 Constellation Simulator: M-ary PSK 🧮 BER calculation for ASK, FSK, and PSK 🧮 Approaches to BER vs SNR What is Bit Error Rate (BER)? The BER indicates how many corrupted bits are received compared to the total number of bits sent. It is the primary figure of merit f...
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AM Modulation Online Simulator

Amplitude Modulation Simulator s AM (t) = A c [1 + k a m(t)] cos(ω c t) where, ω = 2πf & k a = Amplitude Sensitivity Modulation index, μ = k a A m Message Frequency (fm): Carrier Frequency (fc): Carrier Amplitude (Ac): Modulation Index (m = Am / Ac):
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Channel Impulse Response (CIR) (with MATLAB + Simulator)

📘 Overview & Theory 📘 How CIR Affects the Signal 🧮 Online Channel Impulse Response Simulator 🧮 MATLAB Codes 📚 Further Reading What is the Channel Impulse Response (CIR)? The Channel Impulse Response (CIR) is a concept primarily used in the field of telecommunications and signal processing. It provides information about how a communication channel responds to an impulse signal. It describes the behavior of a communication channel in response to an impulse signal. In signal processing, an impulse signal has zero amplitude at all other times and amplitude ∞ at time 0 for the signal. Using a Dirac Delta function, we can approximate this. Fig: Dirac Delta Function The result of this calculation is that all frequencies are responded to equally by δ(t) . This is crucial since we never know which frequenci...
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Online Simulator for ASK, FSK, and PSK

Interactive Digital Signal Processing (DSP) Tutorial and Simulator for ASK, FSK, and BPSK modulation techniques. Try our new Digital Signal Processing Simulator!   •   Interactive ASK, FSK, and BPSK tools updated for 2025. Start Now Digital Modulation Visualizer: ASK, FSK, & BPSK Simulator Learn and visualize binary modulation techniques (ASK, FSK, BPSK) in real-time with adjustable carrier and sampling parameters. Perfect for DSP students and engineers. 📡 ASK Simulator 📶 FSK Simulator 🎚️ BPSK Simulator 📚 More Topics ASK Modulator FSK Modulator BPSK Modulator More Topics 1. ASK (Amplitude Shift Keying) Simulat...
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