Maps continuous (analog) waveform to a corresponding infinite Fourier series of elementary sinusoidal waves Each wave has its on specific amplitude and phase FT converts input signals into a spectrum representation!Īdaptation to sampled finite-duration time-varying signals Same process applied to discrete (digital) signalġ5 How does it work? Imposes sequence of TIME WINDOWS on input signalīreaks signal into “short time” segments Each based on a window function – non-negative and smooth bell- shaped curves Window Function = specific envelope applied to each time window Window duration = 1ms-1sec Each window analyzed separatelyġ6 About windows Used in many different types of processing Essentially says that a complex signal is made up of a sum of simple signals (see below).ġ3 Fourier Transform Mathematical procedure Jean-Baptiste Joseph, Baron de Fourier Fourier Theory Complex vibrations can be analyzed as a sum of many simultaneous simple signals Fourier Analysis = integer relationship between sinusoidal frequenciesġ2 Fourier Theorem Fourier Theorem maintains that a function (or signal) can be described as the sum of a set of simple oscillating functions. Sir Isaac Newton coined term “spectrum” in 1781 describes bands of color frequencies passing through a prism attack) Vibrato and tremolo undulations Perceived loudness Duration Frequency content over time Spectrum = physical property distribution of energy as a function of frequency Timbre = perceptual mechanism that classifies sound into families Amplitude envelope (esp. Timbre Related concepts but not equivalent time Frequency = vertical, time = horizontal amplitude = darknessĩ Spectrum vs. time 2 types Waterfall (time axis moving in real time) Sonogram or spectogram Shows frequency vs. Plotted as 3 dimensional graph of spectrum vs. frequency Measures average energy in each frequency region over the time period of the analyzed segment Ex: PAZ AnalyzerĨ Time-varying plot Depicts varying blend of frequencies over time Spectrum analysis is not a process, but a means of determining sonic contentĤ What is “Spectrum”? Measures the distribution of signal energy as a function of frequencyĥ Spectrum Plots Reveal microstructure of vocal, instrumental and synthetic sounds Reveal characteristic frequency energy of tones Helps identify timbres, or at least characteristics of timbres Often valuable in pitch and rhythm recognitionĪnalyzing spectrum can also help modify/process sounds! Data can be viewed and simply analyzed, OR it can be modified and resynthesized EX: Time Compression/expansion Frequency shifting Convolution Filtering and reverb effects Cross SynthesisĢ-dimensional image of amplitude vs. Presentation on theme: "Spectrum Analysis and Processing"- Presentation transcript:Ģ What is SOUND? Blend of elementary acoustic vibrations combination of sine waves to create more complex soundsģ Spectrum Analysis Viewing the balance among various components of sound Display of frequency content of a sound Each component corresponds to air pressure variation rate Spectrum analysis is useful in determining the spectral content of a sound.
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