Band-Pass Filter
Passes frequencies within a range, attenuates outside. Combination of high-pass and low-pass. Used in audio EQ.
Visualization
Interactive visualization for Band-Pass Filter
Band-Pass Filter:
- • Passes frequencies in range
Interactive visualization with step-by-step execution
Implementation
1function bandPassFilter(signal: number[], lowCutoff: number, highCutoff: number, sampleRate: number): number[] {
2 const highPassed = highPassFilter(signal, lowCutoff, sampleRate);
3 return lowPassFilter(highPassed, highCutoff, sampleRate);
4}
5
6function bandPassSimple(signal: number[], centerFreq: number, bandwidth: number, sampleRate: number): number[] {
7 const lowCutoff = centerFreq - bandwidth / 2;
8 const highCutoff = centerFreq + bandwidth / 2;
9 return bandPassFilter(signal, lowCutoff, highCutoff, sampleRate);
10}Deep Dive
Theoretical Foundation
Band-pass: combines low-pass and high-pass. Center frequency fc, bandwidth BW. H(ω) = H_low(ω) × H_high(ω). Quality factor Q = fc/BW.
Complexity
Time
O(n)
O(n)
O(n)
Space
O(n)
Applications
Industry Use
Audio equalizers and crossover networks
Radio receiver intermediate frequency stages
Voice communication systems
Biomedical signal analysis (EEG bands)
Vibration analysis in specific frequency ranges
Musical instrument isolation in mixing
Use Cases
Related Algorithms
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LCM (Least Common Multiple)
Calculate the Least Common Multiple (LCM) of two integers - the smallest positive integer that is divisible by both numbers. The LCM is intimately related to the GCD through the formula: LCM(a,b) = |a×b| / GCD(a,b). This relationship allows us to compute LCM efficiently using the Euclidean algorithm for GCD, achieving O(log min(a,b)) time complexity instead of naive factorization methods.
Sieve of Eratosthenes
Ancient and highly efficient algorithm to find all prime numbers up to a given limit n. Invented by Greek mathematician Eratosthenes of Cyrene (276-194 BC), this sieve method systematically eliminates multiples of primes, leaving only primes in the array. With O(n log log n) time complexity, it remains one of the most practical algorithms for generating large lists of primes, vastly superior to trial division which runs in O(n² / log n) time.
Prime Factorization
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