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When two signals with these waveforms, same period, and opposite phases are added together, the sum + is either identically zero, or is a sinusoidal signal with the same period and phase, whose amplitude is the difference of the original amplitudes. The phase shift of the co-sine function relative to the sine function is +90°.
A phase-shift oscillator is a linear electronic oscillator circuit that produces a sine wave output. It consists of an inverting amplifier element such as a transistor or op amp with its output fed back to its input through a phase-shift network consisting of resistors and capacitors in a ladder network .
LO is the local oscillator - the carrier sine wave being modulated I(t) and Q(t) are the time-series data for the in-phase and quadrature components. S is the signal . IQ data has extensive use in many signal processing contexts, including for radio modulation, software-defined radio, audio signal processing and electrical engineering.
Tracing the y component of a circle while going around the circle results in a sine wave (red). Tracing the x component results in a cosine wave (blue). Both waves are sinusoids of the same frequency but different phases. A sine wave, sinusoidal wave, or sinusoid (symbol: ∿) is a periodic wave whose waveform (shape) is the trigonometric sine ...
The red line in the waves give the relative phase shift to the other sine waves, originating from the chirp characteristic. The animation removes the phase shift step by step (like with matched filtering), resulting in a sinc pulse when no relative phase shift is left. A chirp signal shares the same spectral content with an impulse signal.
Instantaneous phase and frequency are important concepts in signal processing that occur in the context of the representation and analysis of time-varying functions. [1] The instantaneous phase (also known as local phase or simply phase ) of a complex-valued function s ( t ), is the real-valued function:
By extension, in signal processing a single-frequency tone or pure tone is a purely sinusoidal signal (e.g., a voltage). A pure tone has the property – unique among real-valued wave shapes – that its wave shape is unchanged by linear time-invariant systems ; that is, only the phase and amplitude change between such a system's pure-tone ...
In this particular example, because the output is 90 degrees out of phase from the input, the Lissajous curve is a circle, and is rotating counterclockwise. When the input to an LTI system is sinusoidal, the output is sinusoidal with the same frequency, but it may have a different amplitude and some phase shift.