The following code should be uploaded to the Arduino.

/* Swipe Remote Control

This sketch uses an ultrasonic rangefinder to determine the user's gesture and outputs an IR signal to a sony TV based on the command given.
- High swipe (> 10in) = Channel Up
- Low swipe = Channel Down
- High hold (> 10in) = Volume Up
- Low hold = Volume Down
- Cover sensor (< 3in) = Turn On / Off

Created by Dan Nicholson.

This example code is in the public domain.

This code uses the IRremote library (https://github.com/shirriff/Arduino-IRremote)

*/
#include <IRremote.h>

// Defines for control functions
#define CONTROL_CH 1 // Channel change
#define CONTROL_VOL 2 // Volume
#define CONTROL_POW 3 // Power

#define CONTROL_UP 1
#define CONTROL_DOWN -1

#define DIST_MAX 20 // Maximum distance in inches, anything above is ignored.
#define DIST_DOWN 10 // Threshold for up/down commands. If higher, command is "up". If lower, "down".
#define DIST_POW 3 // Threshold for power command, lower than = power on/off

// IR PIN
const int irPin = 3; // this is defined in the library, this var is just a reminder. CHANGING THIS WILL NOT CHANGE PIN IN LIBRARY
// 2 Pin Ping Sensor
const int pingPin = 8;
const int echoPin = 7;
// Confirmation LED Pins
const int led = 13; //internal LED for up/down debugging
const int ledR = 11;
const int ledG = 10;
const int ledB = 9;
// LED on timer
unsigned long timer;
// IR transmitter object
IRsend irsend;
// Power confirmation flag (needs two swipes to send signal)
boolean powerConfirmed = false;

void setup() {
  // initialize serial communication and set pins
  Serial.begin(9600);
  pinMode(led, OUTPUT);
  pinMode(ledR, OUTPUT);
  pinMode(ledG, OUTPUT);
  pinMode(ledB, OUTPUT); 
  pinMode(pingPin, OUTPUT);
  pinMode(echoPin, INPUT);
  timer = millis();
}

void loop()
{
 
//  Serial.println(millis());
  long duration, inches;
  int value;

  // Check for a reading
  duration = doPing();
 
  // Timer to confirm actions (currently only power)
  if (timer && timer < (millis() - 5000) && (millis() > 5000))
  {
    Serial.println("timer reset");
    timer = false;
  }

   digitalWrite(led, LOW);
   setColor(0, 0, 0); // off

 
  // convert the time into a distance 
  inches = microsecondsToInches(duration);

  // If less than max inches away, act
  if (inches < DIST_MAX)
  {
    // Debug output
    Serial.print(inches);
    Serial.println("in");
   
    // If very close, it is a "power" signal
    if (inches < DIST_POW)
    {
      Serial.println(timer);
      // on or off
      if (timer)
      {
        doIR(CONTROL_POW, 0);
        timer = false;
        delay(2000); // don't want to be sending this more than once. 2 second delay
      }
      else
      {
        Serial.println("power flag set");
        timer = millis();
        setColor(255,50,50);
        delay(500);
      }
    }
    else // is volume or channel
    {
      // Distance determines control direction
      value = handleDist(inches);
      // wait half a second
      delay(300);
      // check again, has hand disappeared?
      if (microsecondsToInches(doPing()) > DIST_MAX)
      {
        doIR(CONTROL_CH, value); // swipe
      }
      else
      {
        // volume
        int d = 500; // first delay is longer for single volume change
        // repeat until hand is removed
        while (inches < DIST_MAX)
        {
          value = handleDist(inches); // is up or down?
          doIR(CONTROL_VOL, value); // fire off IR signal
          delay(d); // wait
          inches = microsecondsToInches(doPing()); // check for hand again
          d = 100; // delays are shorter for quick multiple volume adjustment
        }
        delay(500); // this stops accidental channel change after volume adjustment
      }
    }
  }
  delay(50); // Short enough to detect all swipes.
}
/*
* If distance is within threshold, mark as 'up' and turn on corresponding LED.
*/
int handleDist(int inches)
{
  if (inches > DIST_DOWN)
  {
    digitalWrite(led, HIGH);
    return CONTROL_UP;
  }
  else
  {
    digitalWrite(led, LOW);
    return CONTROL_DOWN;
  }
}

/*
* Fire off correct IR code
*/
void doIR(int control, int val)
{
  switch(control)
  {
  case CONTROL_POW:
    // power
    Serial.println("power on / off 0xa90");
    for (int i = 0; i < 3; i++)
    {
      setColor(255, 0, 0);
      irsend.sendSony(0xa90, 12); // Sony TV power code
      delay(40);
    }
    break;
  case CONTROL_CH:
    setColor(0, 255, 0);
    // output 'channel up / down' depending on val
    if (val == CONTROL_UP)
    {
      digitalWrite(led, HIGH);
      for (int i = 0; i < 3; i++)
      {
        irsend.sendSony(0x90, 12);
        delay(40);
      }
      Serial.println("channel up 0xD00A");
    }
    else // down
    {
      for (int i = 0; i < 3; i++)
      {
        irsend.sendSony(0x890, 12);
        delay(40);
      }
      Serial.println("channel down 0x3002");
    }
    break;
  case CONTROL_VOL:
    setColor(0, 0, 255);
    // output 'volume up / down' depending on val
    if (val == CONTROL_UP)
    {
      digitalWrite(led, HIGH);
      for (int i = 0; i < 3; i++)
      {
        irsend.sendSony(0x490, 12);
        delay(40);
      }
      Serial.println("volume up 0x490");
    }
    else //down
    {
      for (int i = 0; i < 3; i++)
      {
        irsend.sendSony(0xC90, 12);
        delay(40);
      }
      Serial.println("volume down 0xC90");
    }
    break;
  }
}
void setColor(int red, int green, int blue)
{
  analogWrite(ledR, red);
  analogWrite(ledG, green);
  analogWrite(ledB, blue);
}

long doPing()
{
  digitalWrite(pingPin, LOW);
  delayMicroseconds(2);
  digitalWrite(pingPin, HIGH);
  delayMicroseconds(5);
  digitalWrite(pingPin, LOW);
  return pulseIn(echoPin, HIGH);
}

long microsecondsToInches(long microseconds)
{
  // According to Parallax's datasheet for the PING))), there are
  // 73.746 microseconds per inch (i.e. sound travels at 1130 feet per
  // second).  This gives the distance travelled by the ping, outbound
  // and return, so we divide by 2 to get the distance of the obstacle.
  // See: http://www.parallax.com/dl/docs/prod/acc/28015-PING-v1.3.pdf
  return microseconds / 74 / 2;
}

long microsecondsToCentimeters(long microseconds)
{
  // The speed of sound is 340 m/s or 29 microseconds per centimeter.
  // The ping travels out and back, so to find the distance of the
  // object we take half of the distance travelled.
  return microseconds / 29 / 2;
}

Step 4: Let it run!

Controls
The controls are explained in the video, and are as follows:

Power
Swiping over the sensor within 3 inches will cause the LED to flash purple. This is the confirmation that a 'turn on / off' signal is ready to be sent. To prevent it accidentally turning the TV off I have made the sketch wait for a second swipe within 5 seconds of the first to confirm. At this point the signal is sent to the TV to turn on or off.

Channel
Swiping within 10 inches of the sensor (but not within 3)  will cause the channel to change down. Swiping between 10 and 20 inches will cause the channel to change up.

Volume
Holding your hand within 10 inches of the sensor (but not within 3)  will cause the volume to change down. Holding between 10 and 20 inches will cause the volume to change up. The volume will continue to change (up or down) until your hand is removed.