Fourier Transform- Signals and Systems

What is the amplitude and frequency range for ECG?

Amp= 1-2mV (peak to peak)

Freq=0-100 Hz

Name of process ECG goes through to eliminate noise?

Amplification and filtering

What is the amplitude and frequency range for EEG (electro-encephalogram)?

Amp=0-200 microV

Freq=0-50 Hz

Identify the different types of waves within EEG

Alpha waves

Beta Waves

Theta waves

Delta waves

Identify the frequency range and brain activity of alpha waves

8-13 Hz (higher amplitude)

person is awake and relaxed, eyes closed

Identify the frequency range and brain activity of beta waves (1 and 2)

Beta 1= 14-30 Hz (lower amplitude)

Beta 2= 30-50 Hz

related to intellectual activity

Identify the frequency range and brain activity of theta and delta waves and their related brain activity

Theta= 4-7 Hz

Delta= 0.5-3 Hz

both for children when in deep sleep

both present when under general anesthesia

What waves are present when a person is in a coma?

Theta and delta waves

What is Event-related potential testing?

Testing conducted with a pattern of response for a particular stimulus (visual, auditory, tactile, painful) that tells you conduction between type of stimulus and part of brain related to it

If no response, patient is considered brain dead

Describe ECoG (electro-cortico-gram)

Used in neurosurgery, detects brain waves on the surface of the brain

Higher amplitudes due to being inside and closer to the brain (mV)

Frequencies similar to EEG

Describe the range in amplitude and frequencies for EMG (electro-myogram)

For any motion in the muscle

Amp=0-5 mV

freq= 0-1000 Hz (usually between 20-300 Hz)

Describe function of ERG (electro-retino-gram)

Detects potentials produced by retina in response to light stimulus

Describe function of EOG (electro-oculo-gram)

Detects motion of the eye, Voltage goes from positive to negative depending on eye movement

What is the main idea of frequency analysis

A system behaving like a filter for frequencies at the same time responding in time

Time→ Convolution process

Freq→ Transfer function response

Describe the Fourier series

Any signal can be considered a combination of sinusoids with its own amplitude and phase

Established for periodic signals→any periodic signal is a summation of sinusoids

What does Wo represent in Fourier series?

fundamental frequency

Wo= 2pi/T

What does T represent in Fourier series?

Distance from peak to peak

Whar is the assumption for T when signal is not periodic?

T→ infinity

therefore Wo→0

What is the function of Fourier transform?

Works for both nonperiodic and periodic signals

Made for nonperiodic

Transfer of signal into a different domain t→freq and vise versa

What is the difference between direct and inverse Fourier transfrom

Direct= x(t)→X(w) *use tables to solve like Laplace

Inverse= X(w)→x(t)

Describe the purpose of energy in time and energy in frequency

Describes the energy of a signal in its described domain

Obtained using the squared signal magnitude over a given time or frequency interval

Average power of the signal over the signal’s duration

What happens when a sinusoidal signal is transferred into the frequency domain using FT?

Becomes a discrete signal due to frequency domain displaying discrete samples in one cycle of the original sequence

What happens when a pulse is transferred into the frequency domain using FT?

The signal is displayed as the decay of a signal over a cycle, FT converges signal into a continuous spectrum

Achieved through taking the integral of the signal multiplied b complex exponential function

What is a periodic signal?

a type of signal that repeats at regular intervals. Periodic signals are characterized by a constant frequency and may have a constant or varying amplitude

What is a nonperiodic signal?

signals that do not repeat at regular intervals.

What are the two different types of signals

Deterministic (periodic and non periodic)

Stochastic (random)

Name the two types of stochastic signals

Stationary and non stationary

Identify the two types of stationary signals

Ergodic and nonergodic

Most biosignals ergodic

What is a stationary signal

If each section of the signal has the same statistical parameter results than the whole signal

What is an ergodic signal

If all signal recordings have the same statistical results