Electronics & Communication / Sampling Theorem & PAM
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LABORATORY 06 · ELECTRONICS & COMMUNICATION

Nyquist-Shannon Sampling Theorem Verification and Flat-Top PAM Reconstruction

Verify the Nyquist sampling criterion (f_s >= 2 f_m) for flat-top Pulse Amplitude Modulation, observing spectral replication and low-pass filter aperture attenuation. Explore interactive telecommunication simulation, RF analysis, and signal processing telemetry.

ANALOG MODULATION · DIGITAL BASEBAND · PASSBAND MODULATION · ANTENNAS & RF · OPTICAL FIBER · DSP

Your virtual electronics & communication engineering laboratory.

RECONSTRUCTED SIGNAL ATTENUATION A_RECON—
RF INSTRUMENTATION TELEMETRY

Ready to sample with Message Frequency = 1500.0 Hz.

1500.0 Hz
Excitation locked to low-phase-noise synthesized reference oscillator.

Adjust Message Frequency, then execute telecommunication RF/baseband acquisition.

Communication telemetry is sampled with calibrated high-precision instruments using 64-bit IEEE 754 precision buffers. Residuals reflect ordinary least-squares regression across successive observations. Continuous data structures support high-fidelity modulation, channel, and spectral analysis.

Communication engineering assumptions and boundary limits

Channel modeled under additive white Gaussian noise (AWGN) and linear band-limited propagation. Harmonic distortion remains constrained below -45 dBc across all calibrated test points.

Laboratory apparatus & testing equipment.

Sampling Theorem & PAM Telecommunication Workstation

Provides regulated RF/baseband excitation, precision impedance-matched test fixtures, and low-noise interconnection for aliasing distortion, sinc aperture equalization & nyquist rate verification.

6.5-Digit True-RMS Digital Multimeter (Keysight / Fluke)

Measures DC bias points, RMS carrier/signal voltages, and circuit node potentials with ±0.0035% baseline accuracy.

Four-Channel Digital Storage Oscilloscope (200 MHz, 2 GSa/s)

Captures high-frequency RF envelopes, baseband eye diagrams, constellation patterns, and transient responses for sampling theorem & pam.

Synthesized Vector RF Signal Generator (9 kHz – 3 GHz)

Delivers calibrated, low-phase-noise continuous-wave and modulated carrier signals to establish message frequency conditions.

High-Dynamic-Range RF Spectrum Analyzer (9 kHz – 3.6 GHz)

Quantifies fundamental harmonic amplitudes, carrier suppression ratios, sideband power distributions, and spurious emissions.

Matched 50-Ohm Coaxial Interconnects & Attenuator Set

Maintains uniform transmission line impedance, eliminates unwanted standing-wave reflections, and protects instrument front-ends.

FOLLOW THE METHOD

A reason behind every step.

Verify the Nyquist sampling criterion (f_s >= 2 f_m) for flat-top Pulse Amplitude Modulation, observing spectral replication and low-pass filter aperture attenuation. Standardized parameter settings: 500.0, 1000.0, 1500.0, 2000.0, 2500.0, 3000.0 Hz.

  1. Apparatus Calibration & Ground Plane Verification: Inspect all coaxial BNC/SMA interconnects and verify 50-ohm characteristic termination. Power up all instruments and allow a 20-minute thermal settling period to stabilize crystal reference oscillators.
  2. Carrier & Modulating Signal Synthesis: Configure the synthesized RF signal generator and baseband source to the specified baseline parameters. Calibrate the message frequency using the precision digital multimeter and oscilloscope.
  3. Systematic Telemetry Acquisition & Setpoint Stepping: Increment the message frequency systematically across the experimental range (500.0 to 3000.0 Hz), logging the resulting reconstructed signal attenuation a_recon after signal settling.
  4. Frequency-Domain & Time-Domain Cross-Validation: Observe and photograph the corresponding waveform on the digital storage oscilloscope and verify the spectral distribution on the RF spectrum analyzer. Verify that harmonic distortion remains below -45 dBc.
  5. Repeatability & Hysteresis Verification: Execute both ascending and descending parameter sweeps across the device under test (DUT) to detect any thermal drift, detector non-linearity, or oscillator pulling.
  6. De-energization & Dataset Archival: Safely reduce RF excitation levels, save captured digital waveforms to non-volatile storage, export telemetry to the laboratory logbook, and power down all high-frequency instrumentation.
YOUR NOTEBOOK · 0 OBSERVATIONS

Turn measurements into telecommunication engineering insight.

See a complete example report ↗

Points are your recorded observations. The solid regression line validates Sampling Theorem & PAM mathematical scaling.

LINEAR REGRESSION FIT · y = mx + b
A_recon = -0.0025 · f_m + 12.0000
#Message Signal Frequency f_m (Hz)Reconstructed Signal Attenuation A_recon (dB)Message frequency f_m (Hz)Reconstructed attenuation A_recon (dB)

No readings yet. Execute a communication trial and record it.

CHECK YOUR UNDERSTANDING

Explain what the communication metrics mean.

Question 1: In the experimental investigation of Sampling Theorem & PAM, the primary dependent variable measured is:

Question 2: The mathematical relationship governing Sampling Theorem & PAM is modeled as:

Question 3: The target benchmark parameter derived from regression analysis is:

Question 4: Which instrument provides the most accurate visualization of spectral harmonics and carrier sidebands in the frequency domain?

THEORY AND ELECTROMAGNETIC CONTEXT

Electronics & Communication Engineering background & physical principles.

Verify the Nyquist sampling criterion (f_s >= 2 f_m) for flat-top Pulse Amplitude Modulation, observing spectral replication and low-pass filter aperture attenuation.

A_recon = -0.0025 · f_m + 12.0000

Communication systems rely on Fourier spectral decomposition, Shannon channel capacity, and electromagnetic propagation theory.