Spectrum Analyzer
A spectrum analyzer measures and displays the frequency content of a signal, showing amplitude (or power) versus frequency. It reveals which frequencies are present and how strong each is. Types include swept-tuned analyzers (superheterodyne scans across frequencies), FFT analyzers (digitize and compute FFT), and real-time spectrum analyzers (continuous capture). Key specs are frequency range, resolution bandwidth (RBW), dynamic range, and sweep speed.
How a Spectrum Analyzer Works
A traditional swept-tuned spectrum analyzer works like a radio that automatically tunes across all frequencies. It contains a local oscillator that sweeps across a frequency range, mixing with the input signal. When the oscillator frequency matches a signal component, the mixer produces an intermediate frequency (IF) that passes through a narrow bandpass filter. The filter's output is detected and displayed as a peak. Modern FFT-based analyzers digitize the input and compute the discrete Fourier transform, displaying all frequencies simultaneously without sweeping — much faster for capturing transient events.
Key Formulas
Key Specifications: What to Look For
Frequency range determines what signals you can measure — audio analyzers cover 20 Hz to 20 kHz, while RF analyzers span 9 kHz to 40+ GHz. Resolution bandwidth (RBW) is the minimum frequency separation between two distinguishable signals — smaller RBW resolves closer frequencies but slows the sweep. Dynamic range is the ratio between the largest and smallest simultaneously measurable signals — 80 to 120 dB is typical. Phase noise of the local oscillator limits the ability to see weak signals near strong ones.
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Open CalculatorFFT vs. Swept-Tuned Spectrum Analyzers
Swept analyzers look at one frequency at a time, sweeping across the range. They excel at wide frequency spans with excellent dynamic range but can miss brief transient signals. FFT analyzers capture a block of time-domain data and compute all frequencies simultaneously. They catch transients but are limited by ADC dynamic range. Real-time spectrum analyzers (RTSA) combine both advantages: continuous FFTs with overlapping time windows guaranteeing no signal is missed. RTSAs can display spectrograms showing how the spectrum changes over time — essential for analyzing frequency-hopping radios.
Spectrum Analysis in Audio and Music
Audio spectrum analyzers reveal frequency content of sound. A concert A note (440 Hz) shows a peak at 440 Hz plus harmonics at 880, 1320, 1760 Hz — the relative harmonic strengths define timbre. Audio engineers use spectrum analyzers to identify feedback frequencies, check equalization, and ensure balanced mixes. Software spectrum analyzers in DAWs provide this capability at no cost, making frequency analysis accessible to every musician and sound engineer.
The Mathematical Foundation: Fourier Transform
Every spectrum analyzer implements the Fourier transform, decomposing a time-domain signal into frequency components. The continuous Fourier transform F(ω) = ∫f(t)e^{−jωt}dt gives frequency content of analog signals. The DFT X[k] = Σx[n]e^{−j2πkn/N} handles sampled data. The FFT computes the DFT in O(N log N) operations. The Laplace transform generalizes the Fourier transform to complex frequencies, enabling analysis of both frequency content and transient behavior. The LAPLACE Calculator computes these transforms for any function.
Related Topics in signal processing techniques
Understanding spectrum analyzer connects to several related concepts: waveform analyzer, spectrum analysis, spectral analyzer, and frequency analyzer. Each builds on the mathematical foundations covered in this guide.
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