Servo motor noise in analog input

I'm trying to move a servo motor according to an audio stream. But I noticed that as soon as servo gets connected, there is noise in the analog read value. I removed everything and only connected A0 to GND, the servo to 5V, GND and Pin 9, uploaded the below code and watched the serial monitor. I got noise in analog input with average value of 30 and a max of 40. If I remove the servo, I get a flat 0 reading, as expected. Is this behavior expected from a servo and how to prevent it from polluting analog inputs? I tried adding 0.1uF and 10uF caps to servo power pins but was of no use.

-Antzy

#include <Servo.h> 
 
Servo myservo;  // create servo object to control a servo 
 
int pos = 0;    // variable to store the servo position 
int sensorValue;

void setup() 
{ 
  Serial.begin(9600);
  myservo.attach(9);  // attaches the servo on pin 9 to the servo object 
}
 
void loop() 
{ 
  for(pos = 0; pos < 180; pos += 1)  // goes from 0 degrees to 180 degrees 
  {                                  // in steps of 1 degree 
    myservo.write(pos);              // tell servo to go to position in variable 'pos' 

    Serial.print("{");
    Serial.print("input");
    Serial.print(",T,");
    Serial.print(getMaxVal());
    Serial.println("}");
  
  } 
  for(pos = 180; pos>=1; pos-=1)     // goes from 180 degrees to 0 degrees 
  {                                
    myservo.write(pos);              // tell servo to go to position in variable 'pos' 

  
    // print out the value you read:
    Serial.print("{");
    Serial.print("input");
    Serial.print(",T,");
    Serial.print(getMaxVal());
    Serial.println("}");
  }  
}

int getMaxVal()
{
  int maxVal = 0;
  for(int i=0;i<100;i++)
  {
    sensorValue = analogRead(A0);
    if(sensorValue > maxVal)
      maxVal = sensorValue;
  }
  
  return maxVal;
}

I tried powering the servo with a seperate regulated 5V supply and it induced noise in the power supply lines. So when it was drawing power from Arduino, it was possibly changing the Aref voltage causing noise in ADC.

The only mention of electrical noise due to servo on Internet I could find with a solution was:
http://letsmakerobots.com/node/12679
I tried putting caps across power and signal as they suggest but that didn't work.

I found grump mike's decoupling tutorial:
http://www.thebox.myzen.co.uk/Tutorial/De-coupling.html
The capacitors-resistor option didn't work. Will have to buy inductor and give it a try. Has anybody else ever experienced this problem before? I couldn't find many mentions of this on the whole wide Internet.

earth return , star point.