1 Eigenmannia: Glass Knife Fish A Weakly Electric Fish Electrical organ discharges (EODs) – Individually fixed between 250 and 600 Hz –Method of electrolocation.

Slides:



Advertisements
Similar presentations
Physical Layer: Signals, Capacity, and Coding
Advertisements

DCSP-2: Fourier Transform I Jianfeng Feng Department of Computer Science Warwick Univ., UK
What is the neural code? Puchalla et al., What is the neural code? Encoding: how does a stimulus cause the pattern of responses? what are the responses.
Frequency modulation and circuits
1 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen Data Communication, Lecture6 Digital Baseband Transmission.
3. COMPOSITE VIDEO SIGNAL Prepared by Sam Kollannore U. Lecturer, Department of Electronics M.E.S.College, Marampally, Aluva-7.
ECE 6332, Spring, 2014 Wireless Communication Zhu Han Department of Electrical and Computer Engineering Class 13 Mar. 3 rd, 2014.
EE513 Audio Signals and Systems Digital Signal Processing (Synthesis) Kevin D. Donohue Electrical and Computer Engineering University of Kentucky.
STA305 week 31 Assessing Model Adequacy A number of assumptions were made about the model, and these need to be verified in order to use the model for.
Filtering Filtering is one of the most widely used complex signal processing operations The system implementing this operation is called a filter A filter.
TRANSMISSION FUNDAMENTALS Review
LFPs 1: Spectral analysis Kenneth D. Harris 11/2/15.
CHAPTER 4 Noise in Frequency Modulation Systems
Neurophysics Part 1: Neural encoding and decoding (Ch 1-4) Stimulus to response (1-2) Response to stimulus, information in spikes (3-4) Part 2: Neurons.
NOISE and DELAYS in NEUROPHYSICS Andre Longtin Center for Neural Dynamics and Computation Department of Physics Department of Cellular and Molecular Medicine.
Evaluating Hypotheses
Communication Systems
Module 3.0: Data Transmission
Experimental Evaluation
Angle Modulation Objectives
Introduction to Frequency Selective Circuits
Principles of the Global Positioning System Lecture 11 Prof. Thomas Herring Room A;
Noise and SNR. Noise unwanted signals inserted between transmitter and receiver is the major limiting factor in communications system performance 2.
Pulse Modulation 1. Introduction In Continuous Modulation C.M. a parameter in the sinusoidal signal is proportional to m(t) In Pulse Modulation P.M. a.
Formatting and Baseband Modulation
ORE 654 Applications of Ocean Acoustics Lecture 6a Signal processing
Fundamentals of Digital Communication
Sampling Terminology f 0 is the fundamental frequency (Hz) of the signal –Speech: f 0 = vocal cord vibration frequency (>=80Hz) –Speech signals contain.
Random Process The concept of random variable was defined previously as mapping from the Sample Space S to the real line as shown below.
Lecture 1 Signals in the Time and Frequency Domains
COMMUNICATION SYSTEM COMMUNICATION :
Understanding ADC Specifications September Definition of Terms 000 Analogue Input Voltage Digital Output Code FS1/2.
Chapter 6. Baseband Data Transmission. 6.4 Raised-Cosine Pulse Spectrum To ensure physical realizability of the overall pulse spectrum P(f), the modified.
Wireless and Mobile Computing Transmission Fundamentals Lecture 2.
Signal Encoding Techniques. Lecture Learning Outcomes Be able to understand, appreciate and differentiate the different signal encoding criteria available.
Chapter 8 Frequency-Response Analysis
Modern Navigation Thomas Herring
Correlation-Induced Oscillations in Spatio-Temporal Excitable Systems Andre Longtin Physics Department, University of Ottawa Ottawa, Canada.
Design constraints for an active sensing system Insights from the Electric Sense Mark E. Nelson Beckman Institute Univ. of Illinois, Urbana-Champaign.
Signals CY2G2/SE2A2 Information Theory and Signals Aims: To discuss further concepts in information theory and to introduce signal theory. Outcomes:
The Physical Layer Lowest layer in Network Hierarchy. Physical transmission of data. –Various flavors Copper wire, fiber optic, etc... –Physical limits.
Eeng Chapter 5 AM, FM, and Digital Modulated Systems  Phase Modulation (PM)  Frequency Modulation (FM)  Generation of PM and FM  Spectrum of.
EECE 252 PROJECT SPRING 2014 Presented by: Peizhen Sun Nor Asma Mohd Sidik.
Chapter 6. Effect of Noise on Analog Communication Systems
CS Spring 2009 CS 414 – Multimedia Systems Design Lecture 3 – Digital Audio Representation Klara Nahrstedt Spring 2009.
ECE 5525 Osama Saraireh Fall 2005 Dr. Veton Kepuska
1 Quantization Error Analysis Author: Anil Pothireddy 12/10/ /10/2002.
Chapter 11 Filter Design 11.1 Introduction 11.2 Lowpass Filters
Vibrationdata 1 Unit 6a The Fourier Transform. Vibrationdata 2 Courtesy of Professor Alan M. Nathan, University of Illinois at Urbana-Champaign.
ECE 4371, Fall, 2015 Introduction to Telecommunication Engineering/Telecommunication Laboratory Zhu Han Department of Electrical and Computer Engineering.
GG313 Lecture 24 11/17/05 Power Spectrum, Phase Spectrum, and Aliasing.
6. Population Codes Presented by Rhee, Je-Keun © 2008, SNU Biointelligence Lab,
ECE-7000: Nonlinear Dynamical Systems 2. Linear tools and general considerations 2.1 Stationarity and sampling - In principle, the more a scientific measurement.
Part 1 Principles of Frequency Modulation (FM)
Signal Analyzers. Introduction In the first 14 chapters we discussed measurement techniques in the time domain, that is, measurement of parameters that.
4-3-3 Frequency Modulation.. Learning Objectives:At the end of this topic you will be able to; sketch, recognise and analyse the resulting waveforms for.
Comparison Between AM and FM Reception. 21/06/20162 FM Receiver.
Lifecycle from Sound to Digital to Sound. Characteristics of Sound Amplitude Wavelength (w) Frequency ( ) Timbre Hearing: [20Hz – 20KHz] Speech: [200Hz.
UNIT-III Signal Transmission through Linear Systems
Outline Introduction Signal, random variable, random process and spectra Analog modulation Analog to digital conversion Digital transmission through baseband.
Sampling rate conversion by a rational factor
Volume 20, Issue 5, Pages (May 1998)
Volume 20, Issue 5, Pages (May 1998)
Volume 30, Issue 2, Pages (May 2001)
9.4 Enhancing the SNR of Digitized Signals
Jozsef Csicsvari, Hajime Hirase, Akira Mamiya, György Buzsáki  Neuron 
Local Origin of Field Potentials in Visual Cortex
Tuning to Natural Stimulus Dynamics in Primary Auditory Cortex
Daniela Vallentin, Andreas Nieder  Current Biology 
Jan Benda, André Longtin, Leonard Maler  Neuron 
Presentation transcript:

1 Eigenmannia: Glass Knife Fish A Weakly Electric Fish Electrical organ discharges (EODs) – Individually fixed between 250 and 600 Hz –Method of electrolocation and communication Electroreceptors: –Respond to phase (T-type) –Respond to amplitude (P-type)

2 Jamming Avoidance Response Two fish will adjust EOD if frequencies are similar enough. Before: Fish A: 304 Hz, Fish B 300 Hz. After: Fish A: 312 Hz, Fish B 292 Hz. Uses T-type and P-type receptors to compute whether EODs should be raised or lowered. Role of T-type well understood. This paper examines the role of P-type. Electrical Field

3 The P-type Receptor Cells Single afferent projections to Electrosensory Lateral Line (ELL) lobe of the medulla Tuned to the EOD frequency of the individual Loosely phase locked Fire < 1 per electric cycle, though as amplitude increase firings/per cycle goes to one

4 Stimulus and Electrophysiology T = Blank Tape Produces White Noise (the stimulus) –Can vary the Standard Deviation BF = Output passed through low-pass filter with variable cut-food frequency –Can Vary the Cut-Off Frequency (f c ) FG = function generator (next slide) Electrodes in Mouth and Near tail produce electric field, to which receptors respond Insert 1A here

5 The Function Generator A 0 is the Mean Amplitude s(t) is the white noise after it has passed through a filter f carrier is equal to the EOD

6 Recordings Recordings of P-type receptors at the animals trunk Identified P-type receptors by 3 criteria: –Probability of firing per cycle < 1 –Spontaneous activity was irregular –Units phase locked with large jitter 26 units selected Recordings of 135 seconds for 3 Protocols –Spontaneous activity –Response to wide-band white noise (f c = 740 Hz) –Varying f c, A o, and standard deviation of s(t) in a pseudo random manner

7 Theory A linear estimate of the stimulus given the spike train obtained by convolving the spike train with the filter We represent the spike train, resulting from the stimulus, to be t i – spike occurrence time X 0 – mean firing rate.

8 h(t) was chosen to minimize the square error between the stimulus and the stimulus estimate The integration is over the duration of the experiment (T=135sec) fc is cut-off frequency Ssx is Fourier transform of the cross correlation function of the stimulus and the spike train. Sxx is the Fourier transform of the auto correlation function stimulus and the spike train.

9 Now we can determine: We determine “noise”, as the distance between the original stimulus and the estimated stimulus: Signal To Noise Ratio, SNR(f), as the power spectrum of the of the stimulus divided by the power spectrum of the noise Measure the amount of signal power present at a given frequency relative to the noise. SNR = 1 means that it is impossible to differ the signal from the noise.

10 Measure of rate of mutual information that is transmitted by the reconstructions about the stimulus. Dividing by the firing rate λ, yields the mutual information transmitted per spike Is=Ie/ λ Coding Fraction, a normalized measure of the quality of reconstruction ( 0 < γ < 1 ), and for max error γ is 0 (Mean square error in the reconstruction)

11 Data Analysis How we obtained the data for the above equations: Spike Sample: The spike peak occurrences times were selected and resample at 2KHz together with the stimulus.(2KHz because we saw that we are interested in frequencies bellow 740, say 1000 and then nyquist…) Filter: - Estimate of the cross correlation between spike trains and stimulus was obtained by Fast Fourier transform. (S sx,S xx ) SNR: - Estimate of the stimulus and spikes power spectra were obtained using Fast Fourier transform and averaging 130 samples of data, each 1024msec long.

12 The stimulus estimation were obtained by convolving the filter and the spike train in the frequency domain using Fast Fourier Transform. Here to avoid contamination by the carrier frequency of the spike train, they set the filter to zero for frequencies greater than f carrier – 30Hz. Experimental errors were either obtained directly by repeated measurements or by error propagation

13 Results Response to sinusoidal stochastic amplitude modulations – spontaneous activity P-type receptor afferent units fire with increased probability when the amplitude of the external electric field is raised. 10Hz sinusoidal amplitude modulation and the corresponding poststimulus histogram.

14 The spontaneous activity of P units appears consistent with the assumptions of stationary probability density for the spike distribution.

15 Increasing mean stimulus amplitude, increase the probability of firing. A=0.1, λ= 24 A=0.2, λ= 55 A=0.3, λ= 98 A=0.4, λ=112 A=0.5, λ=152 A=0.6, λ=174 A=0.8, λ=208 A=1.0, λ=233

16 Temporal Bandwidth For wide band white noise stimulus 740Hz, checking over 13 units: SNR always equal to 1 for frequencies > 200Hz. and reconstruction is poor γ = (<2.5%) For white noise stimulus 175Hz, while keeping power spectrum constant. SNR improved and more faithful reconstruction γ =

17 Cutoff Frequency The coding fraction γ decreased with increasing fc. Decreasing the fc of the stimulus, increase the SNR at lower frequencies.

18 Why? 1.The power spectra density was increased in the range of frequencies encoded by the units. 2.The power spectra density of the signal was reduced at high frequencies. Two experiments were made to check these assumption. -fc of the stimulus was kept fixed, and the power density was increased. -fc of the stimulus was increased, and the power density was kept constant.

19 Effect of Mean Firing Rate Dynamic Range of mean firing rate from spontaneous firing rate to f carrier (limit once/cycle) Signal-to-Noise Ratio increases as firing rate increases, but saturates at ½ f carrier

20 Coding Fraction, Information Rate, Information Per Spike Coding Fraction, Information Rate also increases and saturates at the same points (Figure a and b), while Information per Spike decreases upon saturation (c) Lower Cut-Off Frequency  Steeper slope in Coding Fraction –f c =175 vs. f c =88 Hz No significant influence of the spontaneous firing rate on the slope of the coding fraction. (Fig. A and B) Significant coding occurred Hz above spontaneous discharge

21

22 Standard Deviation and Signal-to-noise Ratio Varying the Standard Deviation is the same as increasing the amplitude Max. standard deviation set at.25 to avoid phase changes Signal-to-Noise Ratio increases with standard deviation

23 Coding Fraction, Information Rate, Information Per Spike All three of these increase with Standard Deviation Dotted lines are one unit at three mean firing rates (bottom 70, middle 110, and top 170) Larger mean firing rates: –Initial slope larger –Saturation reached at lower standard deviation

24

25 Discussion Studied Encoding Information –Signal-to-Noise –Mutual Information Rate –Coding Fraction Despite the Noise, single afferents encode much of the stimulus

26 Technical Considerations The head and tail electric field geometry most effective in jamming avoidance response They may have chosen T-Type cells, however their data suggest otherwise (P-Type).

27 Reverse Correlation and Linear Reconstruction Filter Spiked were typically triggered by large positive slope in the stimulus. Neither the Biophysical interpretation nor the computational properties that could be read from the filter are obvious. The filter h(t) changes when the statistics of the stimulus or the mean firing rate of the units changes.

28 Their observation of the filter argue against the notion that there is a single cell that explicitly reconstruct the stimulus. The results are true for the assumption that the white noise stimuli is coded with stationary statistics and that the spike train is stationary in response to the stimulus.

29 Existence of nonlinearities The experiment show that adding high frequencies to the stimulus reduce the signal to noise ratio at low frequencies. This indicates that the receptors’ response to electric field amplitude modulation is nonlinear.

30 Natural stimuli 1. A typical power spectrum of natural amplitude modulations around the fish in its natural behavior has not been measured. 2. Amplitude modulations caused by small moving objects have been estimated to be between 2 – 80Hz. They showed that SNR and fraction of signal encoded in single spike trains increase as the cutoff frequency of the stimulus decrease between Hz. (slide18) More experiments were done, decreasing f c to 2, 20, 50 that verified these results.

31 mean firing rate, dynamic range spontaneous activity The mean firing rate λ, increase with the mean amplitude A 0. This enable them to study the coding performances as function of λ by changing A of the stimulus. The SNR, mutual information rate and coding fraction increased with increasing mean firing rate, for firing rates between the spontaneous activity and half of f carrier. Coding started for mean firing rates 20-40Htz above the spontaneous discharge.

32 Coding fraction and mutual information both reached maximum at about half of f carrier. There is a differential sensitivity of the coding fraction and the mutual information transmission as f c of the stimulus was changed. Anesthetized fish have lower spontaneous activity and EOD frequency, thus reduced firing rate than untreated fish, therefore the measured firing rate may not be the optimal one.

33 Standard Deviation and Contrast Coding Fraction, etc. increased with an increase in Standard Deviation Because Mean Firing Rate was constant and only Standard Deviation changed, better performance was not due to more firing

34 Upper Bound on Performance Upper Bound = f carrier because max of one spike per electric cycle Coding fraction at upper bound given by equation below. For these experiments f carrier = 400 Hz and f c = 100 Hz, so coding fraction is 0.75 P receptors can code >1/2 the information that can be encoded about a stimulus

35 Behavioral Relevance Information from the P receptors to the CNS depends on: –Mean firing rate –f c of the stimulus, as will as its contrast –Similar results in mammalian visual system? Individual P receptors covey accurate and efficient representation –Convergence makes more accurate and more efficient?