Example Data Table
| Sample Rate | Samples | Expected Frequency | Expected Period | Suggested Settings |
|---|---|---|---|---|
| 1000 Hz | 30 sine samples | 100 Hz | 0.01 s | Hann, remove mean, padding 4 |
| 8000 Hz | Voice vowel segment | 80 to 300 Hz | 0.0033 to 0.0125 s | Hamming, remove mean |
| 44100 Hz | Tuning tone | 440 Hz | 0.002273 s | Hann, parabolic peak |
Formula Used
The calculator applies a selected window to the input samples. It then computes the discrete Fourier transform.
X[k] = Σ x[n]w[n]e-j2πkn/M
fk = kFs / M
T = 1 / f
|X[k]| = √(Re[k]2 + Im[k]2)
Here, Fs is sample rate. M is DFT size after padding. k is the bin index. The highest selected magnitude gives the dominant sound frequency. The period is its reciprocal.
How to Use This Calculator
Paste sample amplitudes into the sample box. Enter the correct sample rate in hertz. Choose a frequency range that contains the sound period you want. Select a window and detrend option. Use zero padding for smoother peak reading. Press Calculate Period. Use CSV or PDF buttons when you need a file copy.
Understanding Sound Periods With DFT
A sound recording is a list of samples. Each sample stores pressure level at one instant. The sample rate tells how many values were captured each second. The discrete Fourier transform turns those values into frequency bins. Each bin measures how strongly one frequency is present. The strongest useful bin often marks the dominant pitch. Its reciprocal gives the period.
Why Period Matters
Period is the time for one full cycle. A short period means a high tone. A long period means a low tone. Musicians use it to tune notes. Engineers use it to inspect motors, fans, speakers, and vibrations. A stable period can reveal a steady source. A changing period may show modulation, drift, noise, or clipping.
How This Tool Handles Samples
This calculator accepts raw sample values. They may come from a sound editor, sensor log, or generated signal. It can remove the average level. It can also remove a simple straight line trend. Window choices reduce edge jumps. Zero padding adds finer bin spacing. It does not create new information. It only helps locate a peak more smoothly.
Reading The Results
The dominant frequency is chosen from the selected frequency range. The period is one divided by that frequency. The table also shows amplitude, phase, and power for leading bins. Parabolic peak fitting estimates a frequency between two bins. Use it when the peak is clean and isolated. Use direct bin mode for rough or noisy signals.
Good Input Practice
Use enough samples to cover several cycles. Keep the sample rate correct. Avoid clipping when recording sound. Choose a minimum frequency above zero. This avoids selecting slow drift as a pitch. Set a maximum frequency below half the sample rate. That limit follows the Nyquist rule. For speech, music, or machinery, compare several peaks. Real sounds often contain harmonics.
Limits And Checks
A DFT result depends on the record length. Short records have wider frequency bins. Noisy records can hide small peaks. A window may lower apparent amplitude. The calculator corrects for basic window gain. Still, amplitude is an estimate. For critical acoustic work, test with known tones first. Then compare the detected period with measured waveform spacing and timing accuracy.
FAQs
What does this calculator find?
It finds the dominant frequency in sampled sound data. Then it converts that frequency into period. The period shows how long one cycle takes.
Why is sample rate required?
The DFT bin number alone is not a physical frequency. Sample rate converts each bin into hertz. Without it, period cannot be reported in seconds.
Which window should I use?
Use Hann for most sound tests. Use Hamming for similar general work. Use Rectangular when the record contains exact whole cycles. Use Blackman when leakage control matters more.
What is zero padding?
Zero padding adds zeros after your samples before the DFT. It gives closer bin spacing. It helps peak display, but it does not add new measured sound information.
What is parabolic interpolation?
Parabolic interpolation estimates a peak between nearby DFT bins. It can improve frequency and period estimates when the peak is strong, clean, and narrow.
Why remove the mean?
Removing the mean reduces the DC component. This helps prevent a constant offset from masking low frequency sound peaks or sensor vibration patterns.
What frequency range should I enter?
Enter the range where the expected sound exists. Keep the maximum at or below half the sample rate. Raise the minimum to ignore drift.
Can this analyze speech pitch?
It can estimate a dominant period from a short speech segment. Speech is complex, so check harmonics and use enough clean samples.